Inertial Effects on the Stress Generation of Active Fluids

Suspensions of self-propelled bodies generate a unique mechanical stress owing to their motility that impacts their large-scale collective behavior. For microswimmers suspended in a fluid with negligible particle inertia, we have shown that the virial `swim stress' is a useful quantity to understand the rheology and nonequilibrium behaviors of active soft matter systems. For larger self-propelled organisms like fish, it is unclear how particle inertia impacts their stress generation and collective movement. Here, we analyze the effects of finite particle inertia on the mechanical pressure (or stress) generated by a suspension of self-propelled bodies. We find that swimmers of all scales generate a unique `swim stress' and `Reynolds stress' that impacts their collective motion. We discover that particle inertia plays a similar role as confinement in overdamped active Brownian systems, where the reduced run length of the swimmers decreases the swim stress and affects the phase behavior. Although the swim and Reynolds stresses vary individually with the magnitude of particle inertia, the sum of the two contributions is independent of particle inertia. This points to an important concept when computing stresses in computer simulations of nonequilibrium systems---the Reynolds and the virial stresses must both be calculated to obtain the overall stress generated by a system

Swim stress, motion, and deformation of active matter: effect of an external field

We analyze the stress, dispersion, and average swimming speed of self-propelled particles subjected to an external field that affects their orientation and speed. The swimming trajectory is governed by a competition between the orienting influence (i.e., taxis) associated with the external (e.g., magnetic, gravitational, thermal, nutrient concentration) field versus the effects that randomize the particle orientations (e.g., rotary Brownian motion and/or an intrinsic tumbling mechanism like the flagella of bacteria). The swimmers' motion is characterized by a mean drift velocity and an effective translational diffusivity that becomes anisotropic in the presence of the orienting field. Since the diffusivity yields information about the micromechanical stress, the anisotropy generated by the external field creates a normal stress difference in the recently developed “swim stress” tensor [Takatori, Yan, and Brady, Phys. Rev. Lett., 2014]. This property can be exploited in the design of soft, compressible materials in which their size, shape, and motion can be manipulated and tuned by loading the material with active swimmers. Since the swimmers exert different normal stresses in different directions, the material can compress/expand, elongate, and translate depending on the external field strength. Such an active system can be used as nano/micromechanical devices and motors. Analytical solutions are corroborated by Brownian dynamics simulations

A theory for the phase behavior of mixtures of active particles

Systems at equilibrium like molecular or colloidal suspensions have a well-defined thermal energy k_BT that quantifies the particles' kinetic energy and gauges how “hot” or “cold” the system is. For systems far from equilibrium, such as active matter, it is unclear whether the concept of a “temperature” exists and whether self-propelled entities are capable of thermally equilibrating like passive Brownian suspensions. Here we develop a simple mechanical theory to study the phase behavior and “temperature” of a mixture of self-propelled particles. A mixture of active swimmers and passive Brownian particles is an ideal system for discovery of the temperature of active matter and the quantities that get shared upon particle collisions. We derive an explicit equation of state for the active/passive mixture to compute a phase diagram and to generalize thermodynamic concepts like the chemical potential and free energy for a mixture of nonequilibrium species. We find that different stability criteria predict in general different phase boundaries, facilitating considerations in simulations and experiments about which ensemble of variables are held fixed and varied

Towards a 'Thermodynamics' of Active Matter

Self-propulsion allows living systems to display unusual collective behavior. Unlike passive systems in thermal equilibrium, active matter systems are not constrained by conventional thermodynamic laws. A question arises however as to what extent, if any, can concepts from classical thermodynamics be applied to nonequilibrium systems like active matter. Here we use the new swim pressure perspective to develop a simple theory for predicting phase separation in active matter. Using purely mechanical arguments we generate a phase diagram with a spinodal and critical point, and define a nonequilibrium chemical potential to interpret the "binodal." We provide a generalization of thermodynamic concepts like the free energy and temperature for nonequilibrium active systems. Our theory agrees with existing simulation data both qualitatively and quantitatively and may provide a framework for understanding and predicting the behavior of nonequilibrium active systems.Comment: 5 pages, 5 figure

Forces, Stresses, and the (Thermo?) Dynamics of Active Matter: The Swim Pressure

A core feature of many living systems is their ability to move, self-propel, and be active. From bird flocks to bacteria swarms, to even cytoskeletal networks, active matter systems exhibit collective and emergent dynamics owing to their constituents' ability to convert chemical fuel into mechanical activity. Active matter systems generate their own internal stress, which drives them far from equilibrium and thus frees them from conventional thermodynamic constraints, and by so doing they can control and direct their own behavior and that of their surrounding environment. This gives rise to fascinating behaviors such as spontaneous self-assembly and pattern formation, but also makes the theoretical understanding of their complex dynamical behaviors a challenging problem in the statistical physics of soft matter. In this thesis, I present a new principle that all active matter systems display---namely, through their self-motion they generate an intrinsic `swim pressure' that impacts their dynamic and collective behavior. I combine experimental and computational methods to demonstrate how intrinsic activity imparts new behaviors to soft materials that explain a variety of complex phenomena, including the collective motion of self-propelled particles and the complete loss of shear viscosity in fluid suspensions. These nonequilibrium phenomena are driven fundamentally by the active constituent's tendency to diffuse, undergo a random walk, and exert a mechanical force or a pressure on a confining wall. The swim pressure theory is conceptually similar to the kinetic theory of gases, where molecular collisions with the container walls exert a pressure, or to the Brownian osmotic pressure exerted by molecular or colloidal solutes in solution. In contrast to thermodynamic quantities such as the chemical potential and free energy, the mechanical pressure (or stress) is valid out of equilibrium because it comes directly from the micromechanical equations of motion. I apply this swim pressure framework in a broad context to interpret living matter as a material and understand its complex behavior using tools of hydrodynamics, kinetic theory, and nonequilibrium statistical mechanics. The present theory is applied to active systems that are driven by self-propulsion and motility, but there are other types of nonequilibrium driving work that may fit into this general theoretical framework, like driven autocatalytic reactions in electrochemical and biochemical systems.</p

Active surface flows accelerate the coarsening of lipid membrane domains

Phase separation of multicomponent lipid membranes is characterized by the nucleation and coarsening of circular membrane domains that grow slowly in time as $\sim t^{1/3}$, following classical theories of coalescence and Ostwald ripening. In this work, we study the coarsening kinetics of phase-separating lipid membranes subjected to nonequilibrium forces and flows transmitted by motor-driven gliding actin filaments. We experimentally observe that the activity-induced surface flows trigger rapid coarsening of non-circular membrane domains that grow as $\sim t^{2/3}$, a 2$\times$ acceleration in the growth exponent compared to passive coalescence and Ostwald ripening. We analyze these results by developing analytical theories based on the Smoluchowski coagulation model and the phase field model to predict the domain growth in the presence of active flows. Our work demonstrates that active matter forces may be used to control the growth and morphology of membrane domains driven out of equilibrium.Comment: Main text is 5 pages with 3 figures. Supplemental materials attached include a supplemental appendix (includes supplemental movie legends, detailed methods, and derivations) and five supplemental movies (S1-S5

Acoustic trapping of active matter

Confinement of living microorganisms and self-propelled particles by an external trap provides a means of analysing the motion and behaviour of active systems. Developing a tweezer with a trapping radius large compared with the swimmers’ size and run length has been an experimental challenge, as standard optical traps are too weak. Here we report the novel use of an acoustic tweezer to confine self-propelled particles in two dimensions over distances large compared with the swimmers’ run length. We develop a near-harmonic trap to demonstrate the crossover from weak confinement, where the probability density is Boltzmann-like, to strong confinement, where the density is peaked along the perimeter. At high concentrations the swimmers crystallize into a close-packed structure, which subsequently ‘explodes’ as a travelling wave when the tweezer is turned off. The swimmers’ confined motion provides a measurement of the swim pressure, a unique mechanical pressure exerted by self-propelled bodies

In Vivo Oxygen Uptake into the Human Cornea

PURPOSE. We provide a new procedure to quantify in situ corneal oxygen uptake using the micropolarographic Clark electrode. METHODS. Traditionally, upon placing a membrane-covered Clark microelectrode onto a human cornea, the resulting polarographic signal is interpreted as the oxygen partial pressure at the anterior corneal surface. However, the Clark electrode operates at a limiting current. Hence, oxygen flux is directly detected rather than partial pressure. We corrected this misunderstanding and devised a new analysis to quantify oxygen uptake into the cornea. The proposed analysis is applied to new polarographic data for 10 human subjects during open-eye oxygen uptake. RESULTS. Average open-eye corneal oxygen uptake over 10 subjects is approximately 11 lL/(cm 2 h), approximately five times larger than the average reported by researchers who invoke the original mathematical analysis. Application of the classical interpretation scheme to our experimental data also garners uptake values that are approximately a factor of three to five times smaller than those obtained with our new procedure. CONCLUSIONS. The classical procedure originally developed by Fatt and colleagues misinterprets the behavior of the Clark microelectrode. We corrected the analysis of the in situ polarographic technique to provide a simple yet rigorous procedure for analyzing both previous data in the literature and those newly obtained. Our proposed interpretation scheme thus provides a reliable tool for in vivo assessment of corneal oxygen uptake. (Invest Ophthalmol Vis Sci. 2012;53:6331-6337