Emphysematous cystitis with venous bubbles

An 86-year-old nondiabetic woman with an episode of transient ischemic attack two days earlier was referred to our hospital. She had a history of neurogenic bladder and chronic atrial fibrillation and had been anuric for two days. Bubbles were detected by echocardiography in the right atrium, right ventricle, and inferior vena cava. Computed tomography revealed gas accumulation in the wall and lumen of the bladder. She recovered after urinary drainage and antibiotic therapy, and bubbles were no longer detected. It was suspected that bacterial injury of the bladder wall and high intravesical pressure led gas to enter the venous system.     

Capillary equilibrium of bubbles in porous media

In geologic, biologic, and engineering porous media, bubbles (or droplets, ganglia) emerge in the aftermath of flow, phase change, or chemical reactions, where capillary equilibrium of bubbles significantly impacts the hydraulic, transport, and reactive processes. There has previously been great progress in general understanding of capillarity in porous media, but specific investigation into bubbles is lacking. Here, we propose a conceptual model of a bubble’s capillary equilibrium associated with free energy inside a porous medium. We quantify the multistability and hysteretic behaviors of a bubble induced by multiple state variables and study the impacts of pore geometry and wettability. Surprisingly, our model provides a compact explanation of counterintuitive observations that bubble populations within porous media can be thermodynamically stable despite their large specific area by analyzing the relationship between free energy and bubble volume. This work provides a perspective for understanding dispersed fluids in porous media that is relevant to CO₂ sequestration, petroleum recovery, and fuel cells, among other applications.

Bubbles are generated, trapped, and mobilized within porous media as a consequence of incomplete fluid–fluid displacements (1, 2), phase changes (3, 4), chemical and biochemical reactions (5, 6), or injection of emulsified fluids and foams (7, 8). Compared to continuously connected phases, the behavior of dispersed bubbles, or ganglia, are far less understood. In particular, the thermodynamic stability of bubbles, despite their large specific surface area, remains a puzzle. The difficulty comes from the fact that each bubble can attain a volume (V), topology, and capillary pressure (P_c) that is distinct from other bubbles in the medium (9). The variability poses challenges to understanding the transport and trapping mechanisms of bubbles in geologic CO₂ sequestration (10, 11), hydrocarbon recovery (12, 13), fuel cell water management (14, 15), and vadose zone oxygen supply (16, 17).The dominant factor controlling a bubble’s behavior in a porous medium is capillarity, which is typically much larger than either viscous, gravitational, or inertial forces (18, 19). Capillary pressure, P_c, allows a closure relationship for two-phase Darcy Eqs. (20–22) and influences thermodynamic properties like phase partition (23). Capillary pressure is derived from the Young–Laplace equation P_c = γκ, where γ is the interfacial tension and κ is the surface curvature. In an open space without obstacles, a bubble spontaneously evolves into a sphere to minimize its total interfacial energy. Thus, P_c is a continuous and monotonically decreasing function of V (Fig. 1A). However, in a porous medium, bubble’s P_c–V relation is more complicated due to the geometric confinement imposed by the porous structure and topological evolution (24). A bubble can no longer remain spherical as it grows in size but must conform to the geometry of the pore(s) it occupies. Therefore, a bubble’s P_c is a function of not only its volume and interfacial tension but also its topology as dictated by the confining porous medium, as confirmed by recent laboratory experiments and numerical simulations (25–29). The mere presence of confinement therefore engenders a host of phenomena that would otherwise be absent, such as capillary trapping (30, 31), anticoarsening of bubble populations (32, 33), and complex ganglion dynamics (11, 18). Furthermore, theoretical studies in mathematical topology (28, 34, 35) prove that immiscible fluids can be fully characterized by d+1 Minkowski functionals, where d is the problem dimension. Such characterizations remove the path-dependent (or hysteretic) behavior common to these systems (34, 35).Open in a separate windowFig. 1.(A) Spherical bubbles inside a bulk fluid. (B) Micromodel observations show that bubbles are nonspherical in porous media and may occupy multiple pores. This image is from SI Appendix, Movie S1. (C) A 2D porous medium comprised of an ordered array of identical circular grains. A bubble occupying multiple pores including a zoom-in to a portion of it. (D) Illustration of the full state. (E) Illustration of the critical state. (F) Decomposition of a bubble into four distinct parts: minor arc menisci shown by dark blue cap-shaped regions, throats shown by light blue diamond-shaped regions, inner bulk bodies shown by red star-shaped regions, and major arc menisci shown by dark green cap-shaped regions.Recent developments in microfluidics and micro computed tomography imaging allow detailed pore-scale visualizations of fluids inside porous media, including the morphology of bubbles and ganglia (25, 36–39). Garing et al. (25) experimentally measured the equilibrium capillary pressure of trapped air bubbles inside sandstone and bead-pack samples. They found that, unlike bubbles within a bulk fluid, the P_c of trapped bubbles shows no clear dependence on V and seems to fall within a bounded interval, except for vanishingly small V. Xu et al. (40) proposed an empirical correlation for the P_c trapped bubbles based on microfluidic observations. In this correlation, as V increases, P_c decreases until a minimum is reached and then increases linearly. In the first stage, the bubble is unconfined, whereas in the second, it is reshaped by the surrounding solid walls. The proposed correlation, however, is only valid for bubbles in a single pore and not bubbles that span multiple pores. The latter seems to be rather common in nature as evidenced by recent direct observations (Fig. 1B) (2, 25).Here, we propose a simple conceptual model to describe the equilibrium states of a bubble with arbitrary size trapped inside a porous medium. The model accounts for the bubble’s morphology, the geometry of the solid matrix, and the wettability between the two. We derive all metastable configurations of the bubble analytically and highlight the thermodynamic states the bubble assumes when it is static, growing, or shrinking. We also show that the relationship between surface free energy (F) and volume (V) of large bubbles is approximately linear, which explains the previously counterintuitive observation that such bubbles are thermodynamically stable despite having large surface areas. Our work provides a step toward understanding the capillary state, stability, and evolution of dispersed immiscible fluids in porous media.     

Photodrive of magnetic bubbles via magnetoelastic waves

Precise control of magnetic domain walls continues to be a central topic in the field of spintronics to boost infotech, logic, and memory applications. One way is to drive the domain wall by current in metals. In insulators, the incoherent flow of phonons and magnons induced by the temperature gradient can carry the spins, i.e., spin Seebeck effect, but the spatial and time dependence is difficult to control. Here, we report that coherent phonons hybridized with spin waves, magnetoelastic waves, can drive magnetic bubble domains, or curved domain walls, in an iron garnet, which are excited by ultrafast laser pulses at a nonabsorbing photon energy. These magnetoelastic waves were imaged by time-resolved Faraday microscopy, and the resultant spin transfer force was evaluated to be larger for domain walls with steeper curvature. This will pave a path for the rapid spatiotemporal control of magnetic textures in insulating magnets.To materialize integrated spintronics (1, 2), it is essential to avoid excess energy to generate the control magnetic field by electric current. Therefore, the practical manipulation of the magnetic domain wall (DW) is now being realized by spin transfer torque generated from spin-polarized charge current in metals (3) and from flow of magnons in insulators (4), e.g., via the spin Seebeck effect (5, 6). On the other hand, the optical control, aiming at ultrafast, nonthermal, and remote access to magnetic domains, remains elusive even after the discoveries of photomagnetic domain manipulation (7, 8), laser-induced magnetization reversal (9), and directional generation of magnetostatic waves (10). The main difficulty has been due to the weak coupling between photon and spin; in general, only a fraction of total spin moment can be modulated by visible–to–near-infrared photoexcitation if one wants to avoid extensive heating in the electron/lattice sectors. Here, we report an alternative optical process of generating coherent magnons, via magnetoelastic couplings as originally proposed by Kittel (11), and their interaction with magnetic domains, with a special attention to the geometry of the DWs.A magnetic bubble generally refers to a cylinder-like magnetic domain formed by long-range dipolar interactions, in which the magnetization is antiparallel to external magnetic field at the center and is parallel at its periphery with various types of DW spin windings. Having experienced an intense study in the 1960s and 1970s for nonvolatile memory applications (12), there is a recent reawakening of interest in magnetic bubbles, owing to the experimental discovery of magnetic skyrmions in noncentrosymmetric helimagnets with relativistic Dzyaloshinskii–Moriya (DM) interactions (13–15). These skyrmions have noncoplanar spin-swirling textures, wrapping the unit sphere an integer number of times (15), and can be topologically equivalent to magnetic bubbles without Bloch lines at the wall (called type I) (16). One apparent difference shows up in their size; the diameter of skyrmions by the DM interaction typically ranges from 3 to 200 nm, whereas those by dipolar interaction from 100 nm to several micrometers (15). Various emergent interactions characterizing skyrmions have been revealed recently, such as the topological Hall effect, skyrmion Hall effect, and multiferroic behaviors in the insulating background, etc., some of which can be visualized under the Lorentz transmission electron microscope as current-driven and magnon-driven kinetics (17, 18). With the emergent electromagnetism induced by its steric and topological spin alignments, the skyrmion can function as an externally operable information carrier. From the viewpoint of topology, the dynamics of the magnetic bubble have direct relations with those of the skyrmion, with a definite advantage that bubbles can readily be observed under polarized optical microscopes. By convention, we refer to the circular magnetic domains in iron garnets as magnetic bubbles in the following, although some of them can be called skyrmions as well.One can manipulate magnetic bubbles by external magnetic-field gradients or thermal ones; the latter have been realized by heating the sample by a focused laser (heat mode) at absorbing photon energy, creating a gradient of the order of 10 K/μm (19, 20). On the other hand, it has been demonstrated that skyrmions formed by the DM interaction can be driven through the interaction with spin-polarized charge current of ultralow density (∼10⁶ A⋅m⁻², five to six orders of magnitude smaller than that for the DW motion in ferromagnets) (17, 21), or by thermally excited magnon flow (18), owing to their emergent electromagnetic responses (15).Considering the recent advances in the ultrafast optical control of spin ensembles (22), as well as in the understanding of interactions of spin wave and spin current with magnetic nanostructures, it is interesting to examine the photon–bubble (or photon–skyrmion) interaction. In particular, we focus on the magnetoelastic wave, a propagating mode of coupled sound and spin waves, which is capable of carrying a spin excitation more efficiently than thermally excited incoherent phonons. A phonon is a quantum of the lattice distortion wave, and a magnon is that of the spin wave. In a magnet, the crystal lattice experiences a small deformation when magnetized; such magnetostriction depends on the crystal symmetry and the direction of magnetization in the presence of spin–orbit interaction. When a sound wave travels in this magnetic crystal, the propagating lattice distortion tilts the spin out from its equilibrium direction through the magnetoelastic coupling (11). This coupling is enhanced at the resonant magnetoelastic mode when the original dispersions of phonon and magnon cross. The interaction between magnetoelastic waves and magnetic bubbles in insulating iron garnets as shown below will be readily generalized to the case of skyrmions in insulating chiral magnets.     

Localization of denaturation bubbles in random DNA sequences

We study the thermodynamic and dynamic behaviors of twist-induced denaturation bubbles in a long, stretched random sequence of DNA. The small bubbles associated with weak twist are delocalized. Above a threshold torque, the bubbles of several tens of bases or larger become preferentially localized to AT-rich segments. In the localized regime, the bubbles exhibit "aging" and move around subdiffusively with continuously varying dynamic exponents. These properties are derived by using results of large-deviation theory together with scaling arguments and are verified by Monte Carlo simulations.     

Flowering in bursting bubbles with viscoelastic interfaces

The lifetime of bubbles, from formation to rupture, attracts attention because bubbles are often present in natural and industrial processes, and their geometry, drainage, coarsening, and rupture strongly affect those operations. Bubble rupture happens rapidly, and it may generate a cascade of small droplets or bubbles. Once a hole is nucleated within a bubble, it opens up with a variety of shapes and velocities depending on the liquid properties. A range of bubble rupture modes are reported in literature in which the reduction of a surface energy drives the rupture against inertial and viscous forces. The role of surface viscoelasticity of the liquid film in this colorful scenario is, however, still unknown. We found that the presence of interfacial viscoelasticity has a profound effect in the bubble bursting dynamics. Indeed, we observed different bubble bursting mechanisms upon the transition from viscous-controlled to surface viscoelasticity-controlled rupture. When this transition occurs, a bursting bubble resembling the blooming of a flower is observed. A simple modeling argument is proposed, leading to the prediction of the characteristic length scales and the number and shape of the bubble flower petals, thus paving the way for the control of liquid formulations with surface viscoelasticity as a key ingredient. These findings can have important implications in the study of bubble dynamics, with consequences for the numerous processes involving bubble rupture. Bubble flowering can indeed impact phenomena such as the spreading of nutrients in nature or the life of cells in bioreactors.

When residing in Newtonian fluids, bubble rupture proceeds with features that are shown in Fig. 1. Different dynamics are observed depending on the capillary number, Ca=u η/γ, where u is the experimentally measured characteristic retraction speed of the film, η is the liquid viscosity, and γ is the surface tension between the liquid and gas, and the Reynolds number, Re=ρuRbubble/η, where ρ is the liquid density, and Rbubble is the bubble radius (1–7). Fig. 1 A–D report observed bubble ruptures in the different regimes previously discussed in the literature: 1) for Re≪1, viscous forces are larger than inertial and surface forces, resulting in a very slow hole opening (8) (Fig. 1A); 2) when Re>1, the hole opens up much more quickly (9), and a toroidal rim (Fig. 1B) is subjected to an azimuthal instability, which leads to fingering and, possibly, jetting (Fig. 1 B–D), depending on the corresponding Ca value. If Ca≫1, the rim is stable and folds upward (10); otherwise, inertial instabilities break it into pieces with a characteristic length scale, d=Rbubbleh, where h is the film thickness (11).Open in a separate windowFig. 1.Bubble bursting dynamics. (A) Low Re. (B and C) High Ca and high Re. (D) Low Ca and high Re. (E) Low Ca and high Re with intermediate interfacial viscoelasticity (20 mg/mL of BSA). (F) Low Ca and high Re with high interfacial viscoelasticity (50 mg/mL of BSA). (G) Bubble rupture as functions of time for different concentrations of BSA. Increasing the concentration of BSA leads to an increase in the surface viscoelasticity, and the bubble bursting dynamics change. The concentration of 20 mg/mL is identified as the limit above which flowering occurs. The number of petals, 10 at 20 mg/mL, decreases to 5 when the concentration of BSA is increased to 50 mg/mL. The bursting time (from the puncture to complete film retraction) increases when BSA is added, and it changes from 1.5 ms at 0.1 mg/mL to 2.7 ms at 50 mg/mL.Here, we report evidence of the effect of surface viscoelasticity in bubble rupture dynamics. Surface viscoelasticity is adjusted by adding a surface-active material to the bulk and modulating its concentration and chemistry. We chose bovine serum albumin (BSA) proteins (12, 13), as they are known to form highly viscoelastic surface layers. At low concentrations, BSA molecules are adsorbed at the air/water interface with their major axis parallel to the surface. No protein denaturation occurs, and the molecules retain their globular conformation. As the concentration of BSA increases, a primary monolayer achieves full surface coverage, and a secondary monolayer appears, extending into the aqueous phase (14, 15). Adsorbed protein molecules are connected by interprotein contacts forming an interconnected network within the adsorbed layers (16). Upon compression, globular proteins, such as BSA, respond as deformable spheres, thereby being capable of storing elastic energy (yielding high storage moduli) (17). Many examples can be found in the literature in which the addition of surfactants to the protein solution can drastically change surface properties, giving an unlimited variety of model systems to achieve desired surface properties with a straightforward tuning of the surfactant concentration (18).     

From the Cover: Ethnic diversity deflates price bubbles

Markets are central to modern society, so their failures can be devastating. Here, we examine a prominent failure: price bubbles. Bubbles emerge when traders err collectively in pricing, causing misfit between market prices and the true values of assets. The causes of such collective errors remain elusive. We propose that bubbles are affected by ethnic homogeneity in the market and can be thwarted by diversity. In homogenous markets, traders place undue confidence in the decisions of others. Less likely to scrutinize others’ decisions, traders are more likely to accept prices that deviate from true values. To test this, we constructed experimental markets in Southeast Asia and North America, where participants traded stocks to earn money. We randomly assigned participants to ethnically homogeneous or diverse markets. We find a marked difference: Across markets and locations, market prices fit true values 58% better in diverse markets. The effect is similar across sites, despite sizeable differences in culture and ethnic composition. Specifically, in homogenous markets, overpricing is higher as traders are more likely to accept speculative prices. Their pricing errors are more correlated than in diverse markets. In addition, when bubbles burst, homogenous markets crash more severely. The findings suggest that price bubbles arise not only from individual errors or financial conditions, but also from the social context of decision making. The evidence may inform public discussion on ethnic diversity: it may be beneficial not only for providing variety in perspectives and skills, but also because diversity facilitates friction that enhances deliberation and upends conformity.In modern society, markets are ubiquitous (1). We rely on them not only to furnish necessities but also to finance businesses, provide healthcare, control pollution, and predict events (2). The market has become such a central social institution because it typically excels in aggregating information and expectations from disparate traders, thereby setting prices and allocating resources better than any individual or government (3). However, markets can go astray, and here we examine a prominent failure of markets: price bubbles (4–6).Bubbles emerge when traders err collectively in pricing, causing a persistent misfit between the market price and the true value (also known as “intrinsic” or “fundamental” value) of an asset, such as a stock (7, 8). Bubbles devastate individuals and markets, wreck nations, and destabilize the entire world economy. When a stock market bubble burst in 1929, the Great Depression materialized (6). After its “bubble economy” ruptured in 1990, Japan stagnated for decades. More recently, housing bubbles in the United States and Europe caused a financial crisis, burdening the global economy since (3, 7).Price bubbles can wreck people, markets, and nations, but they also present a puzzle. That people occasionally err is unsurprising—psychologists and economists have documented myriad individual biases—but individual errors do not necessitate a bubble. Traders vie for advantage, so if some unwittingly misprice an asset, for example by paying lofty prices, competitors should exploit the error by offering to sell dearly, thereby profiting from others’ mistakes (9). At the same time, the sellers also increase supply and depress prices, which should prevent a bubble. In other words, even if some traders err, the market as a whole should still price accurately—markets are thought to be self-correcting (3). For price bubbles to emerge, pricing errors must be not idiosyncratic, but common among traders.Attempting to pinpoint the cause of bubbles, some researchers have designed experimental markets that are ideally suited for accurate decision making. However, even there—with skilled participants who possess complete information about the true values of the stocks traded—bubbles persist (7, 8). Researchers have shown that bubbles are related to financial conditions such as excess cash (10), but also to behavior that exhibits “elements of irrationality” (11). Indeed, bubbles have been long ascribed to collective delusions, implied in terms such as “herd behavior” and “animal spirits” (12–14), but their exact causes remain nebulous. We suggest that that price bubbles arise not only from individual errors or financial conditions but also from the social context of decision making.We draw on studies that have used simulations (15), ethnographic accounts of an arbitrage disaster (9), and qualitative research on the recent financial crisis (16) that point to the dangers of homogeneity. We also rely on past research investigating the effects of diversity on the performance of countries and regions, organizations, and teams. Our results suggest that bubbles are affected by a property of the collectivity of market traders—ethnic homogeneity.Homogeneity and diversity have been studied across the social sciences. A commonly accepted view is that cognitive diversity, an assortment of perspectives and skills, enables exchange of valuable information, thereby enhancing creativity and problem solving (15, 17). However, when it comes to ethnic diversity, the effects are decidedly mixed. Ethnic diversity has been studied in multiple spheres, including economic growth (18, 19), social capital (20), cities and neighborhoods (21), organizations (17, 22), work teams (23–25), and jury deliberations (26). Some studies find benefits, but others do not. For instance, ethnic diversity in a city or region can summon a multitude of abilities, experiences, and cultures, but can also bring heterogeneity in preferences and mores, which complicates public policy decisions (18, 27) and may hamper collective action (20). In the workplace, ethnic diversity is associated with greater innovation, but also increased conflict (28).Some of the disparity can be explained by the results we report here: Ethnic diversity facilitates friction. This friction can increase conflict in some group settings, whether a work team, a community, or a region (29). Conversely, ethnic homogeneity may induce confidence, or instrumental trust (30), in others'' decisions (confidence not necessarily in their benevolence or morality, but in the reasonableness of their decisions, as captured in such everyday statements as “I trust his judgment”). However, in modern markets, vigilant skepticism is beneficial; overreliance on others’ decisions is risky.As Portes and Vikstorm (31) note, modern “markets do not run on social capital; they operate instead on the basis of universalistic rules and their embodiment in specific roles.” In other words, modern markets rely less on the mechanical solidarity engendered by coethnicity, the “bounded solidarity” (32) embodied for instance in the Maghribi traders’ coalition (33) or the rotating credit associations of Southeast Asia (34, 35). Instead, modern markets rely on organic solidary, which turns on heterogeneity, role differentiation, and division of labor (31, 36). Ethnic homogeneity may be beneficial in some group settings for the same reason it may be detrimental to modern markets—it instills confidence in others’ decisions.Confidence in others’ decisions matters because, in many situations, people watch others for cues about appropriate behavior (37). When people enter a market, whether to purchase stock, buy a house, or hire an employee, they heed not only the objective features of the good or service—the performance of the company, the number of bedrooms, the years of work experience—but they also note the behavior of others, attempting to decipher their mindset before deciding how to act (12, 13, 38). In a modern market, where competition is key, undue confidence in others’ decisions is counterproductive: It can discourage scrutiny and encourage imitation of others’ decisions, ultimately causing bubbles.In ethnically homogenous markets, we propose, traders place greater confidence in the actions of others. They are more likely to accept their coethnics’ decisions as reasonable, and therefore more likely to act alike. Compared with those in an ethnically diverse market, traders in a homogenous market are less likely to scrutinize others’ behavior. Conversely, in a diverse market, traders are more likely to scrutinize others’ behavior and less likely to assume that others’ decisions are reasonable.This proposition is galvanized by a persistent empirical finding across the social sciences: People tend to be more trusting of the perspectives, actions, and intentions of ethnically similar others (21, 39, 40). As intergroup contact theory and social identity theory establish, shared ethnic identity is a broad basis for establishing trust among strangers. Moreover, empirical evidence shows specifically that people surrounded by ethnic peers tend to process information more superficially (26, 41, 42). Such superficial thinking fits with the notion of greater confidence in others’ decisions: If one assumes that others’ decisions are reasonable, one may exert less effort in scrutinizing them. For instance, ethnically diverse juries consider a wider range of perspectives, deliberate longer, and make fewer inaccurate statements than homogeneous juries (26). Compared with those in homogeneous discussion groups, students who are told they will join diverse discussion groups review the discussion materials more thoroughly beforehand (42) and write more complex postdiscussion essays (41). In markets, where information is incomplete and decisions are uncertain (43), traders may be particularly reliant on ethnicity as a group-level heuristic for establishing confidence in others’ decisions. Such superficial information processing can engender conformity, herding, and price bubbles. As the term implies, herding is not the outcome of careful analysis but of observational imitation (14).Therefore, we propose that, when an offer is made to buy or to sell an asset, traders in homogeneous markets are more likely to accept it than those in diverse markets. If traders in homogeneous markets place greater confidence in the decisions of their coethnics, so they are more likely to accept offers that are further from true value. This is not an individual idiosyncrasy, but a collective phenomenon: Pricing errors of traders in homogenous markets are more likely to be correlated than those of traders in diverse markets. The culmination of these processes leads to bubbles that are bigger.To study the effects of diversity on markets, we created experimental markets in Southeast Asia (study 1) and North America (study 2). We selected those locales purposefully. The ethnic groups in them are distinct and nonoverlapping—Chinese, Malays, and Indians in Southeast Asia, and Whites, Latinos, and African-Americans in North America—thus allowing a broad comparison. We also sought more generalizable results by including participants beyond Western, rich, industrialized, and democratic nations (44).Realistic trading requires financial skills, so we turned to those who are likely to possess it. For study 1, in Southeast Asia, we recruited skilled participants, trained in business or finance, for a “stock-trading simulation.” We surveyed their demographics in advance and randomly assigned them to markets (trading sessions) as to create a collectivity of traders that was either ethnically homogeneous or diverse (Fig. 1). In the homogeneous markets, all participants were drawn from the dominant ethnicity in the locale; in the diverse markets, at least one of the participants was an ethnic minority. All traders could view their counterparts and note the ethnicities present in the market.Open in a separate windowFig. 1.The experiment. Participants were randomly assigned to markets that were ethnically homogeneous or diverse (Left). After they received the information needed to price stocks accurately, we assessed each participant’s financial skills individually, using 10 hypothetical market scenarios to establish a baseline of pricing accuracy (Center). Trading in a computerized stock market, each participant was free to buy and sell stocks and/or to make requests to buy (“bid”) or offers to sell (“ask”). All trading information was true, public, and anonymous: All participants could see all completed transactions and bid and ask offers (Right; see example in SI Appendix, Fig. S8). The data reflect actual prices in the sixth period of trading in two of the markets of study 1. The experiment did not involve deception.When the participants arrived in the trading laboratory, we provided them with all of the information necessary to calculate the stocks’ true value accurately, including examples. After they read the instructions (and before actual trading), we assessed each participant’s comprehension and financial (pricing) skills. We presented each participant separately with simple market scenarios and asked him or her to declare the prices in which he or she would buy or sell in each scenario. The participants could not see the others’ responses. We used the responses to calculate ex-ante pricing accuracy: the extent to which the participants’ responses, in aggregate, approximated the true values of the stocks. This measure of pricing accuracy serves as a baseline of performance. Because the responses were collected individually, and participants could not observe others’ responses, social influence was minimal at this stage. Fig. 1 provides a visual overview of the experiment.Next, participants were allocated cash and stocks and began trading. Much as in a modern stock market, participants observed all of the trading activity on their computer screens. They saw the prices at which others bid to buy and asked to sell. They saw what others ultimately paid and received. As various financial features of the market can affect bubbles (45–47), we control these through the experimental design. While trading, participants could not see each other or communicate directly. As in modern stock markets, they did not know which trader made a certain bid or offer. So, direct social influence was curtailed, but herding was possible. When trading ended, the participants received their earnings in cash. Then, we used the prices in which stocks were bought and sold to calculate the ex-post pricing accuracy: the extent to which market prices, on average, approximated the true values of the stocks.For study 2, a replication in North America, we followed the same protocol. An exact, or direct, replication further suggests that the pattern we observed is general, independent of specific culture or demographics (48). So we selected a wholly different site, distinct by culture and encompassing a different mix of ethnicities.     

Simulation of exchanges of multiple gases in bubbles in the body

This communication introduces a system of equations, for numerical solution, which simulates the generation, growth, and decay of bubbles. The system is an advance over previous works because it allows for simultaneous diffusion of any number of gases. Our purpose for developing the system is to gain insight into the bubbles that occur in the body in decompression sickness (DCS). We validate the calculation system by matching observed data of DCS bubbles and of large subcutaneous gas pockets in rats. We demonstrate how a temporary supersaturation and bubble formation can occur without change of ambient pressure when there is a change in the inert gas being breathed. With exposures to hypobaric environments, such as when astronauts work in space, simulations show that O₂, CO₂, and water vapor add appreciably to volume of bubbles and affect the diffusion of inert gas.     

Surface tension, proteinuria, and the urine bubbles of Hippocrates

Hippocrates noted that bubbles in urine were associated with kidney disease. We examined changes in surface tension responsible for bubble formation in urine, to investigate whether surface tension could be a more accurate and continuous linear predictor of 24-h proteinuria than currently available tests on spot urine.     

Determining hydrodynamic forces in bursting bubbles using DNA nanotube mechanics

Quantifying the mechanical forces produced by fluid flows within the ocean is critical to understanding the ocean’s environmental phenomena. Such forces may have been instrumental in the origin of life by driving a primitive form of self-replication through fragmentation. Among the intense sources of hydrodynamic shear encountered in the ocean are breaking waves and the bursting bubbles produced by such waves. On a microscopic scale, one expects the surface-tension–driven flows produced during bubble rupture to exhibit particularly high velocity gradients due to the small size scales and masses involved. However, little work has examined the strength of shear flow rates in commonly encountered ocean conditions. By using DNA nanotubes as a novel fluid flow sensor, we investigate the elongational rates generated in bursting films within aqueous bubble foams using both laboratory buffer and ocean water. To characterize the elongational rate distribution associated with a bursting bubble, we introduce the concept of a fragmentation volume and measure its form as a function of elongational flow rate. We find that substantial volumes experience surprisingly large flow rates: during the bursting of a bubble having an air volume of 10 mm³, elongational rates at least as large as ϵ˙=1.0×108 s⁻¹ are generated in a fragmentation volume of  ～ 2 × 10^?6 μL. The determination of the elongational strain rate distribution is essential for assessing how effectively fluid motion within bursting bubbles at the ocean surface can shear microscopic particles and microorganisms, and could have driven the self-replication of a protobiont.Functioning like a giant heat engine between the high-temperature heat bath of the sun and the low-temperature heat bath of outer space, the earth’s atmosphere generates wind and rain with intense fluid flows. The mechanical stresses produced by these hydrodynamic flows are among the environmental stresses that biological organisms must cope with. Organisms often exploit these stresses and fluid flows, most notably to aid reproduction. A well-known example at the macroscopic scale is the wind dispersal of spores, seeds, and pollen. Less well-known, fragmentation resulting from fluid-flow-induced stress is used by a number of marine organisms as a means of vegetative reproduction, such as macrophyte algae (1) and sponge and coral colony (2, 3) propagation by storm-induced fragmentation. Can analogous mechanical forces facilitate vegetative reproduction at the microscale? Current evidence is at best indirect: Filamentous cyanobacteria are known to fragment under environmental stress (4, 5), suggesting that prokaryotes may use fluid-flow-induced fragmentation as a means of clonal reproduction and dispersal as well.Several origin-of-life hypotheses invoke processes in which environmentally produced microscale mechanical forces drive self-replication through fragmentation. Oparin proposed that fragmentation of coacervates may have constituted a primitive form of self-replication allowing for Darwinian evolution by natural selection (6). More concretely, Cairns-Smith proposed that life arose from mineral crystals that replicated by fragmentation into new seed crystals, thereby propagating genetic information consisting of the patterns of defects within the mother crystal (7–9). Szostak’s group also proposed that division of protocells (having a lipid bilayer) can be driven by fluid flow (10–12). Inspired by Cairns-Smith’s proposal, Schulman, Yurke, and Winfree used DNA tile self-assembly to construct a self-replicating system in which fragmentation was induced by intense elongational flow at a constriction in a flow channel (13). This synthetic system is analogous to an in vitro system in which exponential growth of prions is driven via fragmentation by mechanical shearing of amyloid fibrils (14). Similarities between regeneration (self-healing) and asexual reproduction in modern organisms have led some to postulate fragmentation-and-regeneration as a primordial form of reproduction (15).To effectively shear microscopic objects such as bacteria or protobionts, fluid flows must exhibit high-velocity gradients over the length scale of the object. Such small-scale high-velocity-gradient flows occur naturally in breaking ocean waves that produce whitecaps (16). Within these waves, the highest velocity gradients are expected to occur in the films of bursting bubbles due to the rapid acceleration produced by surface tension forces acting on the small fluid mass. Moreover, bursting bubbles can generate mechanical stresses of sufficient intensity to be biologically relevant to organisms living in the sea surface microlayer (neuston) (17). As a technological example, cell death at the air–liquid interface during the sparging of bioreactors to enhance oxygen diffusion has been attributed to bubble bursting (18).The fluid flows most effective at shearing small free-floating objects are those that exhibit strain deformation. In such flows, a rod-shaped object will tend to align itself along the direction of maximum fluid extension. In this orientation the rod experiences the greatest tensile stress and is most susceptible to fragmentation. In a given fluid element, the rate of fluid extension––i.e., the rate at which two points in the fluid separate, divided by the distance between them––has a maximum that is referred to as the elongational rate and is here denoted by ϵ˙. A useful way to conceptualize the meaning of ϵ˙ is to consider the case when it is constant. In this case, the time it takes for the fluid element to double its length is tb=ln(2)/ϵ˙.Fig. 1 shows a mechanism by which rod-shaped objects within bursting fluid films can be fragmented. As the hole produced in the bubble film expands, its circumference increases (Fig. 1B). Due to this, fluid elements near the hole’s edge will experience elongation in the direction perpendicular to the velocity of the hole edge. As shown in Fig. 1 C and D, rod-shaped structures within the bubble film will align along the circumference of the expanding hole. If the tension generated along the length of the structure exceeds its tensile strength, the structure will fragment (Fig. 1E).Open in a separate windowFig. 1.DNA nanotubes fragmentation by bursting bubbles. Side (A) and top (B) views of a bubble filled with air bursting on a water surface. Color gradient loosely corresponds to the expected magnitude of the hydrodynamic forces. (B–E) As the hole travels outward driven by surface tension, the liquid film is accumulated into a growing toroidal rim (gray rings). The enlargement of the hole produces elongational flow, with rate ϵ˙=v/r, which is tangential to the perimeter where r is the hole radius and v is the outward velocity of the hole perimeter. The two blue arcs are the two volume elements of the bursting film. (C and D). As the hole expands, the fluid flow orients DNA nanotubes (black, red). (D and E) The elongational flow breaks sufficiently long DNA nanotubes (black) of length l into fragments of length l₁ and l₂ due to tension applied to the nanotube by the elongational fluid flow. Short nanotubes (red) are not fragmented due to insufficient build-up of tension.The elongational rates generated by this mechanism can be estimated using a model of film hole dynamics, for a film of uniform thickness. Initially considered by Dupré (19), Rayleigh (20), and Ranz (21), then corrected by Culick (22) and Taylor (23), the model treats the rupture as a circular hole that propagates outward with the film fluid accumulating in a toroid at the hole perimeter. From momentum balance, the hole propagates outward with a constant speed v=2σ/ρδ, where σ is the surface tension of the film, ρ is the fluid density, and δ is the film thickness. The elongational rate of the circumference is given by ϵ˙=v/r, where r is the hole radius. The volume of fluid subjected to elongational rates greater than ϵ˙, in this simple model, is given by Vf(ϵ˙)=πδr2=2πσ/ρϵ˙2, which is, surprisingly, independent of film thickness. Such volumes provide a natural way to characterize the ability of a bursting bubble to fragment objects suspended within the bubble film that will shear under given elongational rate ϵ˙. Importantly, Vf(ϵ˙) can be defined in a model-independent way as the volume of fluid that experiences elongational rates greater than ϵ˙ during the course of bubble bursting. We will refer to such volumes as fragmentation volumes.Although easiest to explain, the Culick and Taylor model does not describe the only type of elongational flow that can be generated within a bursting bubble; therefore the estimate for Vf(ϵ˙) based on this model should be considered a loose lower bound for the true value. In fact, only half the surface-tension energy released is converted into the kinetic energy of the outward motion of the fluid (24). This suggests that the other half of the surface-tension energy must be dissipated within the film near the edge of the hole. For fluids with low viscosity, such as water, this implies that there are intense small-scale fluid flows near the edge of the hole (18) in addition to those illustrated in Fig. 1. Hydrodynamic instabilities, particularly with larger bubbles, can occur along the perimeter, resulting in fingering and the formation of droplets (25). Also, particularly for small bubbles, the expanding hole produces an inward propagating wave at the bottom surface of the bubble that forms a jet that may launch droplets (26, 27). High-flow gradients are expected in the region where these jets pinch to form droplets. A recent discussion of droplet production during bubble bursting in ocean-like (i.e., not soapy) water was given by Lhuissier and Villermaux (28).As discussed by Lhuissier and Villermaux, at the instant the bubble bursts it possesses a cap of uniform thickness that, at a well-defined edge, joins with the bulk fluid in a region where the thickness rapidly increases with distance from the center of the bubble (Fig. 1A). The critical thickness at which bubble films spontaneously burst depends on the bubble radius (28), increasing from 0.05 to 30 μm as the bubble radius increases from 1 to 20 mm. For an object such as a microorganism to be fully impacted by the mechanical stresses produced by bubble bursting, it would have to reside in the cap film or close to the cap boundary; that is, its thinnest dimension would have to be smaller than the film thickness. Nevertheless, mechanical stresses produced by bursting bubbles are among the stresses that microorganisms, particularly those that occupy the niche consisting of the neuston or sea surface microlayer (29–31), must cope with. We hypothesize that protobionts, small enough to be suspended within the bubble film, also occupied this niche and used these stresses to facilitate replication. However, little work seems to have been done to characterize the elongational rates produced during the bursting of a bubble that would facilitate assessing whether forces of sufficient magnitude are generated.In this study the fragmentation of DNA nanotubes is used to characterize both the magnitude of the elongational rates produced and the volume of fluid subjected to these elongational rates during bubble bursting. These nanotubes are constructed from short DNA oligomers referred to as single-stranded tiles, which each have four sequence domains by which a given oligomer binds with four neighboring oligomers via Watson–Crick base pairing. Thus, whereas each DNA oligomer is held together by covalent bonds, the entire tube assembly is held together by the supramolecular interactions that enable two complementary single-stranded oligomers to form duplex DNA. Base sequences of the oligomers are designed so that the axes of the duplex DNA are parallel to the long axis of the tube. The supramolecular Watson–Crick bonds between neighboring single-stranded tiles are much weaker than the covalent bonds of the phosphate backbone of a single-stranded tile (32). Under sudden tension along the axis of the duplex DNA (33), the tensile force at which the supramolecular bonding fails is referred to as the overstretching force f_c, which has a value of about 65 pN (34, 35). For a tube in which there are n duplex strands in cross-section, the tensile force will be T_c = nf_c. For the tubes used in the experiments reported here, n = 7 (SI Appendix, Fig. S1) and consequently the tubes fragment when subjected to tensile forces in excess of 455 pN. The tubes have a radius of 4 nm, a persistence length of 5 μm (36), and a length distribution that peaks at 5 μm at the start of the experiment (SI Appendix, Fig. S2; see Fig. 3 B and G).Open in a separate windowFig. 3.Nanotube length distributions for bubble bursting experiments in assay buffer or in ocean water. Fluorescence microscopy images and fragment length distributions of DNA nanotubes withdrawn from a sample with an initial volume of 100 μL after 0 mL (A and B), 60 mL (C and D), and 360 mL (E and F) of air had passed through the sample at a flow rate of 18 mL/min. The mean tube length ?l? for each distribution is given at the top of each histogram. Nanotube length distribution in bubble bursting experiment with ocean water after 0 mL (G), 60 mL (H), and 360 mL (I) of air.Some of these tubes will be trapped in the bubble film and will be subjected to elongational forces in the manner illustrated in Fig. 1. Although nanotubes will necessarily also be subject to compressive fluid flows, they are not fragile under compression. The junctions at which a given single-stranded tile connects with two neighboring tiles are flexible, allowing the tube to crumple and then straighten when the compressive forces are relieved. This collapse into a coil configuration followed by stretching has been studied for other stiff linear biopolymers and synthetic fibers in hydrodynamic flows near stagnation points (33, 37, 38). Generally, the tubes will crumple under the compressive flow and reorient and stretch along the axis of the elongational flow (Movie S1 and SI Appendix, section 10). A further complication is that Brownian motion will tend to counteract the alignment produced by the elongational flow. However, as will be shown, under the conditions in which our DNA nanotubes break, the Péclet number––which is the ratio of the active transport rate to the diffusive transport rate––is in excess of 1.4 × 10⁴, indicating that diffusive misalignment of the nanotubes plays a negligible role in our experiments. Due to the viscous stresses exerted on the DNA nanotube as it reorients along the direction of maximum extension flow, the tension experienced by the tube will be greatest at the center of the tube and will be greater for longer tubes, scaling as T∝ϵ˙l2/ln(l/2R), where l is the tube length and R the tube radius (34). If the tensile force is exceeded, the tube will break into two fragments of nearly equal length. If the elongational flow continues to intensify so that the two fragments experience a tension at their centers that exceeds the tensile force, each of these in turn will fragment into two shorter pieces of equal length. This cascading process will continue until the elongational rate reaches its maximum value.DNA nanotubes are well-suited to serve as probes of hydrodynamic flows within bubble films for three reasons. First, their fragmentation in elongational flows has already been extensively characterized (34). Second, they are highly soluble in water and do not exhibit a surfactant-like tendency to stick to the air–water interface, unlike many proteins. Third, it is straightforward to measure histograms of nanotube lengths using fluorescence microscopy. Here, from the evolution of the DNA nanotube fragment length during the course of bubbling, we were able to determine the fragmentation volumes for elongational rates over five orders of magnitude, although our experimental techniques were not able to distinguish where the DNA nanotubes were broken within the bubble. Our findings suggest that, via bubbles, ocean waves provide a source of strong mechanical forces at the micron-scale mechanical stresses that ocean surface-dwelling microbes must cope with, that may be involved in the natural breakdown of pollutants, and that would have been available for protobionts to use as a means of driving self-replication.     

Flow field around bubbles on formation of air embolism in small vessels

An air embolism is induced by intravascular bubbles that block the blood flow in vessels, which causes a high risk of pulmonary hypertension and myocardial and cerebral infarction. However, it is still unclear how a moving bubble is stopped in the blood flow to form an air embolism in small vessels. In this work, microfluidic experiments, in vivo and in vitro, are performed in small vessels, where bubbles are seen to deform and stop gradually in the flow. A clot is always found to originate at the tail of a moving bubble, which is attributed to the special flow field around the bubble. As the clot grows, it breaks the lubrication film between the bubble and the channel wall; thus, the friction force is increased to stop the bubble. This study illustrates the stopping process of elongated bubbles in small vessels and brings insight into the formation of air embolism.

Air embolism is the entrapment of air bubbles into vascular structures (1, 2). It often happens in therapeutic procedures such as injection and surgeries (3, 4). It also occurs in diving or aerospace activities in which the environmental pressure changes rapidly (5). The air embolism often causes tissue ischemia and results in myocardial infarct or brain damages (6, 7). In clinical studies (8–10), it is common to find that a single bubble is trapped in a small vessel with diameter of the order of 100 μm to form an air embolism. However, it is still unknown how the bubble is brought to rest in small vessels and what the effect of the fluid dynamics on the stopping process is. The understanding of the fluid dynamics of a moving bubble confined in a small vessel will bring insight on the mechanism of the air embolism and is also crucial to the prevention and treatment of the air embolism.The air embolism has been well studied when a bubble is trapped in a vessel and contacts the endothelial layer (11–13). However, it is still unclear how a bubble moving along with the continuous blood flow stops in the vessel. It is usually believed that the bubble is stopped by the friction force on it. However, according to Taylor and Bretherton’s theory (14, 15), a bubble will become a Taylor bubble, which is deformed and elongated, when it flows in a smaller channel, and a thin lubrication film of the surrounding liquid will form around it. Therefore, the bubble will keep flowing without contacting the channel wall. The Laplace pressure from the bubble surface is considered another reason to stop the bubble. When a bubble encounters a junction of the vessel, the Laplace pressure caused by the deformation of surface at the head of the bubble may be able to overcome the blood pressure (16). However, when the radius of the vessel is equal to or greater than 100 μm, the Laplace pressure of the bubble is lower than 1 kPa, which is much less than the driving pressure, ∼10 to 15 kPa, in the small arteries (17). In the other case, when a bubble is moving in a small vessel, the confined bubble surface results in higher pressure within the bubble, which will squeeze the lubrication film to build up drag resistance. However, it is also too low to stop the bubble. To reveal the dominant reason a bubble would stop in small vessels, the braking process of the bubble needs to be observed and studied. However, it is still difficult to show the motion of a bubble and its surrounding flow fields in small vessels. The current methods, such as computed tomography, contrast-enhanced ultrasound, magnetic resonance images, and echocardiography (18–20), are not able to provide a high-resolution flow field around the moving bubble.In this work, in vivo and in vitro experiments are performed to show the motion of a bubble during its braking process in the small vessels. Microfluidic devices are made to show the flow field around a moving bubble, and the effect of the flow field on the coagulation on the bubble surface is illustrated. During the coagulation, the variation of the lubrication film and the corresponding friction force on the bubble are both measured to explain the reason for the stopping of the bubble.In Vivo Observation on Formation of Air EmbolismFormation of an air embolism is observed in vivo in the mesenteric vascular network of a rabbit. Blood mixed with air bubbles is injected into mesenteric vascular vessels of the rabbit, and the motion of a bubble in a small vessel is then observed by a fluorescent microscope. The schematics of the experiment are shown in Fig. 1 A and B, and the experimental details are introduced in Materials and Methods.Open in a separate windowFig. 1.In vivo experiment of air embolism formed in mesenteric vascular vessels of a rabbit. (A) Schematics of the in vivo experiment. (B) Schematics of the flow fields around a flowing bubble confined in a vessel and the aggregation of RBCs on the bubble surface. (C) The combined images of the stopping process of a bubble flowing in a small vessel in time series. The red color is the reflection of light from the bubble surface, which indicates the position of the bubble. The video of the moving bubble is provided in Movie S1. (D) The velocity of the bubble at the locations of 1 to 5 as marked in image C. (E) Masson-stained histological section of the air embolus taken from the vessel along the flow direction, and F is the clot formed at the tail of the bubble, corresponding to the location in the dashed box in E. (The scale bars in C–F are 100 μm.)In a vessel with the diameter of 200 μm, an injected bubble that reflects the red color is observed to flow through two junctions and finally stop in the vessel to form an air embolus, as shown by a combined image of the time series of the moving bubble in Fig. 1C, where the bubble flows from location 1 to location 5 with variation in its shape. In addition, the velocities of the bubble at the five locations are shown in Fig. 1D. The in vivo experiment clearly shows that a bubble deforms into a Taylor bubble and flows as a slug flow in the small vessel (21), in which the bubble is squeezed to form a long bubble and followed by a segment of liquid. The bubble gradually comes to rest in the vessel. This result is different from the suggestion that an air embolism is caused by a spherical bubble as soon as it forms from the dissolved gas in blood (2), and the shape of the bubble observed in this experiment is consistent with the studies reported before (22–24). The dynamic observation provides the details about the process of how the Taylor bubble transports, deforms, and finally stops in the small vessel.The air emboli formed in small vessels in vivo are taken out to be examined under a microscope. It is interesting to find that the clot is formed at the tail of the bubbles, as shown by the histological section of the air embolus in Fig. 1 E and F. The section is stained by Masson and red blood cells (RBCs), and the fibrin are found in the section of the clot. The clot formed at the tail illustrates that the coagulation happens unevenly on the bubble, and it indicates that the flow field around the bubble plays an important role. This finding has not been reported in previous studies including clinical anatomy (1–3) and rheological experiments (25, 26). In clinical anatomy, a thin layer consisted of cells and fibrins is also found on the bubble surface but it is observed on the cross-section of the vessel, and the uneven distribution of the clot on the bubble along the flowing direction is not seen. In rheological experiments (25, 26), the Couette flow is different from the slug flow for a Taylor bubble; thus, the clot is not formed at the tail of the bubble.This finding raises another interesting question: Does the clot form to stop the bubble, or does the bubble stop to form the clot? Although the uneven distribution of the thrombus on the bubble indicates that the clot starts to form when the bubble is moving, it is still necessary to observe the coagulation on a bubble during its stopping process. Since it is difficult to observe the coagulation and the flow field in vessels, in vitro experiments are performed as follows.In Vitro Experiments on an Air Embolism T-junction polydimethylsiloxane PDMS) microchannel is fabricated according to the soft photolithography method (27), and its cross-section and the size are shown in Fig. 2A. The inner surface of the channel is coated by bovine serum albumin (BSA) to avoid coagulation. The fibrinogens in the injected blood are dyed (Materials and Methods), which will emit red fluorescence when they are cross-linked into fibrin once the coagulation occurs. Blood and air are injected into the channel through separated inlets. At the junction of the channels, bubbles are formed with the size controlled by the flow rate ratio of the blood to the air. According to the observed bubble in the in vivo experiment, the bubble length in the channel is controlled to be ∼3 to 5 times larger than the channel size. The flow velocity of the blood is 7.0 mm/s, which is in the order of 10 mm/s of the blood flow in arterioles with the diameter of 0.2 mm (28, 29).Open in a separate windowFig. 2.In vitro experiments of the air embolism performed on microfluidic devices. (A) The cross-section of the channel is square, and it is coated with a BSA layer. (B and C) The origin and growth of the blood clot at the tail of a bubble at the different positions as marked in A. (D) The velocity of the bubble during its stopping process. (E) A bubble passes through the channel without stopping in glycerol solution. (F) A microfluidic vessel network with a four-level structure. (G) Bubbles pass through the network in glycerol solution. (H and I) Bubbles pass through the second to third levels but stop in the fourth level. (Scale bars, 200 μm.)Firstly, the formation of an air embolism is observed in the devices. In the transparent channel, the origin of a clot at the tail of an injected bubble can be seen clearly during the stopping process of the bubble, as shown in Fig. 2 B and C. When the bubble enters the channel, it elongates, and the flow becomes a slug flow. The coagulation does not happen on the bubble surface yet and there is no fluorescence around the bubble. As the bubble is flowing, fluorescence appears to indicate the formation of a clot at the tail of the bubble, as shown in Fig. 2B, and the speed of the bubble is found to decrease as shown in Fig. 2D. As the clot grows at the tail, it finally stops the motion of the bubble at the curved section of the channel, as shown in Fig. 2 C and D.This experiment clarifies that the coagulation happens on the bubble surface when the bubble is still moving in the vessel, and the coagulation on the bubble affects the braking of the bubble. To validate the effect of the coagulation on the slowing down of the bubble, blood is replaced by glycerol water solution with the same viscosity (η ∼4 mPa ⋅ s), and bubbles are seen to flow through the channel rapidly without stopping, as shown in Fig. 2E. It validates that the coagulation on the bubble surface is a dominant factor during the formation of an air embolism in a small vessel.Furthermore, a channel network is fabricated to simulate a more complex vascular network. The PDMS channel network has 4 levels with the sizes of 500, 240, 150, and 100 μm for each level, as shown in Fig. 2F. When the continuous phase is the glycerol solution, the bubbles are observed to flow through the network without stopping under the driven pressure of 10 kPa, as shown in Fig. 2G. The corresponding video is provided in Movie S2. However, when the blood is used, the bubbles stop in the fourth level and clots are found on their surface, as shown in Fig. 2 H and I, respectively. The video is provided in Movie S3.In the in vitro experiments, the origination of the clot at the tail of the bubble is clearly illustrated by the fluorescence during the stopping process of the bubble in the channel, which repeats the same results with those found in the in vivo experiments. They also reveal the relationship between the coagulation on the bubble surface and the stopping of the bubble. It confirms that, in the slug flow, the coagulation is the dominant factor for the stopping of the bubble instead of the Laplace pressure.Secondly, the flow field around the bubble is measured to explain why the clot originates at the tail of the bubble. The transparent microchannel makes it possible to measure the flow field around the bubble during its stopping process. To see the flow field more clearly, diluted blood with hematocrit (HCT) of 1% is used in the measurement. The motion of the RBCs around a flowing bubble is captured by a high-speed camera. The flow field is derived in Micro-Particle Image Velocimetry software (Materials and Methods).At the tail of the bubble, there are a pair of recirculation zones of the blood flow, as shown in Fig. 3A. Near the bubble surface, most of the blood is flowing toward the bubble, which brings blood cells onto the bubble surface. In contrast, on the head of the bubble, there are also a pair of recirculation zones of the blood flow, but most of the blood is flowing away from the bubble, thus the cells are pushed away from the bubble surface. With respect to the bubble surface, the opposite-flowing direction of the blood explains why the clot is formed at the tail of a flowing bubble. The measured flow field around the bubble is consistent with the fluidic model established in droplet microfluidics, as shown by the schematics in Fig. 3B (30). The mechanism has been studied by Stebe in the research of remobilizing the surfactant concentration at the bubble interface (31), and a similar flow field has been visualized by Yamaguchi using microparticle image velocimetry (32). On the bubble surface, there are six stagnant points (i)-(vi). That means that particles on the surface will be brought toward these points. Among them, points (iv) and (vi), which are part of a ring on the rear caps of the bubble, are kinematically stable points. Thus, the blood cells and fibrinogens driven by the flow will move toward the two points and aggregate there. To show the aggregation of particles on the bubble surface more clearly, larger poly methyl methacrylate particles with the size of 20 μm are used in the experiment. The microparticles are observed to aggregate at the points (iv) and (vi) at the tail of the bubble, as shown in Fig. 3C. The same effect can be seen in the experiments with RBCs and other sizes of particles, which are shown in SI Appendix, Fig. S2. The result confirms that the flow fields around the bubble carries blood cells and fibrinogens to the stagnant points, and the aggregation of the cells and fibrinogens at the points causes the formation of fibrins and the origination of clot at the tail of a moving bubble.Open in a separate windowFig. 3.Flow field around a moving bubble and the formation of the cell aggregation at the tail. (A) Measured flow fields around the tail and the head of the bubble. The black points on the background are the RBCs. (B) Schematics of the flow field around the bubble surface and the stagnant points on the bubble surface. (i) through (vi) are stagnant points, and only (iv) and (vi) are kinematically stable points. (C) Poly methyl methacrylate particles are seen to adhere on the stable stagnant points at the tail of a moving bubble. (D) Blood cells and fibrin (marked in the circles) are flowing in the lubrication film from the head to the tail of the bubble. (Scale bars, 100 μm.)Under the influence of the flow field, the cell aggregation is observed to extend backward (opposite to the flow direction), as well as forward (along the flow direction), which is shown in Movie S4. The reason for the cell aggregation to grow backward is attributed to the flow field behind the bubble that keeps bringing cells to the tail of the bubble. The forward growth of the cell aggregation is attributed to the flow along the head-to-tail streamlines on the bubble surface, as shown in Fig. 3B, which brings cells from the head of the bubble. According to the lubrication theory by Bretherton (17), there is a lubrication film between the bubble and the wall, which provides a gap for the cells on the head to move to reach the tail of the bubble.In the experiment, blood cells are seen to flow from the head to the tail on the bubble surface, as shown in Fig. 3D. However, the number of cells traveling in this way is quite low. This can be attributed to the Fåhræus-Lindqvist Effect (33), which causes a decrease of RBC concentration (hematocrit level) when the blood flows from the channel to the thin lubrication film. When the cells reach the tail of the bubble, they will be stopped by the cell aggregation already formed there; thus, the cell aggregation will extend forward through the gap between the bubble and the wall. It should be noted that the forward growth of the cell aggregation is much slower than the backward growth because most of the cells near the head of the bubble are flowing away from the bubble surface along the streamlines and only a few cells reaching the head of the bubble can flow to the tail along the head-to-tail streamlines.The measured flow field around the bubble shows the aggregation of the blood cells. The aggregation points around the bubble are consistent with the locations where the fluorescent labeled fibrins appear. It reveals the close relation between the motion of blood cell driven by the flow and the formation of clot around the bubble. It explains why the clot originates at the tail of the bubble, and it clearly demonstrates that the fluid dynamics of the slug flow play a dominant role in the formation of air embolism.Lubrication Film and Friction Force MeasurementAlong with the aggregation of blood cells and fibrinogens, the fibrins appear, and then the clot grows on the bubble surface. The clot occupies part of the space of the lubrication film around the bubble, and the friction force on the bubble increases to stop the bubble, as shown in Fig. 4A. The lubrication film around the bubble is measured during the growth of the clot using an interference method (34). The thickness of the lubrication film is calculated according to the interference fringes, as shown in Fig. 4 B, i and ii. The details on the measurement and the calculation are provided in SI Appendix. As the clot grows, a dark region appears at the tail of the interference fringes, as shown in Fig. 4C. It indicates that there is no lubrication film in this region and the clot on the bubble contacts the wall of the channel. The length of the contacting region is evaluated by the contact length l_c.Open in a separate windowFig. 4.The measured lubrication status and the friction force on the bubble. (A) Schematics of the lubrication status of a bubble changed by the clot on the bubble surface. (B, i and ii) The interference fringes of the lubrication film measured when the bubble starts to flow and when it is pushed to flow again after its first stop in the channel, respectively. (Scale bar, 100 μm.) (C) The derived film thickness and the contact length corresponding to the fringes in B, i and ii. (D) The measured driving pressure to overcome the friction resistance under the different contact length in the push-stop experiment, ∼1 to 5 indicates 5 groups of repeated experiments.The change of the friction force on the bubble is measured during the variation of the lubrication film using a push-stop method. A controlled pressure is applied at the inlet to push the bubble to move in the channel. When the bubble stops because of the growth of the clot on its surface, the pressure is increased until the bubble is pushed to move again. As soon as the bubble is moved by the increased pressure, the contact length of the bubble is recorded. The product of the increased pressure and the cross-sectional area of the channel equals to the maximum static friction force on the bubble. As the cross-sectional areas of channels are kept unchanged in these experiments, the increased pressure is directly used to represent the friction resistance to the motion of the bubble. Using this push-stop method, the friction resistances on the air emboli with the different contact length are obtained. They clearly show that the growth of the clot changes the lubrication status of the bubble. The increased friction force between the bubble and the channel will stop the bubble to cause air embolism in the channel.     

带子瘤颅内动脉瘤的壁面切应力分析

目的探讨带子瘤颅内动脉瘤的壁面切应力（WSS）特点。方法结合数字减影血管造影（DSA）三维图像,采用计算流体力学（CFD）有限元方法的软件,对7例带子瘤的颅内动脉瘤行血流动力学数值模拟,对其WSS进行分析,并与临床资料作对比分析。结果心动周期内,每例患者子瘤处的WSS明显低于母瘤（P〈0．01）。相对于其他时刻,T=0．2s时,动脉瘤WSS最高（P〈0．05）。结论子瘤的WSS明显低,容易破裂。