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Register a new userOnsagers variational principle in active soft matter
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Onsagers variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, $Phys. Rev.$, 1931, $37$, 405]. This fundamental principle provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially in the study of soft matter dynamics. In this work, OVP is extended and applied to the dynamic modeling of active soft matter such as suspensions of bacteria and aggregates of animal cells. We first extend the general formulation of OVP to active matter dynamics where active forces are included as external non-conservative forces. We then use OVP to analyze the directional motion of individual active units: a molecular motor walking on a stiff biofilament and a toy two-sphere microswimmer. Next, we use OVP to formulate a diffuse-interface model for an active polar droplet on a solid substrate. In addition to the generalized hydrodynamic equations for active polar fluids in the bulk region, we have also derived thermodynamically consistent boundary conditions. Finally, we consider the dynamics of a thin active polar droplet under the lubrication approximation. We use OVP to derive a generalized thin film equation and then employ OVP as an approximation tool to find the spreading laws for the thin active polar droplet. By incorporating the activity of biological systems into OVP, we develop a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.
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In this review we summarize theoretical progress in the field of active matter, placing it in the context of recent experiments. Our approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of the review is to integrate the several approaches proposed in the literature, from semi-microscopic to phenomenological. In particular, we first consider dry systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium, and clarify the differences and similarities between two types of orientationally ordered states, the nematic and the polar. We then consider the active hydrodynamics of a suspension, and relate as well as contrast it with the dry case. We further highlight various large-scale instabilities of these nonequilibrium states of matter. We discuss and connect various semi-microscopic derivations of the continuum theory, highlighting the unifying and generic nature of the continuum model. Throughout the review, we discuss the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular materials. We suggest promising extensions towards greater realism in specific contexts from cell biology to ethology, and remark on some exotic active-matter analogues. Lastly, we summarize the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents.
Recent progress in the understanding of the effect of electrostatics in soft matter is presented. A vast amount of materials contains ions ranging from the molecular scale (e.g., electrolyte) to the meso/macroscopic one (e.g., charged colloidal particles or polyelectrolytes). Their (micro)structure and physicochemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular theoretical and simulational aspects, including the experimental motivations, will be discussed.
We generalize an idea in the works of Landauer and Bennett on computations, and Hills in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity $ ablawedgebig(mathbf{D}^{-1}mathbf{b}big)$ and vorticity potential $mathbf{A}(mathbf{x})$ of the stationary flux $mathbf{J}^{*}= ablatimesmathbf{A}$. Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsagers reciprocality; the scalar product of the two bivectors $mathbf{A}cdot ablawedgebig(mathbf{D}^{-1}mathbf{b}big)$ is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that maps vorticity to cycle affinity is introduced.
Soft materials such as colloidal suspensions, polymer solutions and liquid crystals are constituted by mesoscopic entities held together by weak forces. Their mechanical moduli are several orders of magnitude lower than those of atomic solids. The application of small to moderate stresses to these materials results in the disruption of their microstructures. The resulting flow is non-Newtonian and is characterised by features such as shear rate-dependent viscosities and non-zero normal stresses. This article begins with an introduction to some unusual flow properties displayed by soft matter. Experiments that report a spectrum of novel phenomena exhibited by these materials, such as turbulent drag reduction, elastic turbulence, the formation of shear bands and the existence of rheological chaos, flow-induced birefringence and the unusual rheology of soft glassy materials, are reviewed. The focus then shifts to observations of the liquid-like response of granular media that have been subjected to external forces. The article concludes with examples of the patterns that emerge when certain soft materials are vibrated, or when they are displaced with Newtonian fluids of lower viscosities.
We present a comprehensive review of the physical behavior of yield stress materials in soft condensed matter, which encompass a broad range of materials from colloidal assemblies and gels to emulsions and non-Brownian suspensions. All these disordered materials display a nonlinear flow behavior in response to external mechanical forces, due to the existence of a finite force threshold for flow to occur: the yield stress. We discuss both the physical origin and rheological consequences associated with this nonlinear behavior, and give an overview of experimental techniques available to measure the yield stress. We discuss recent progress concerning a microscopic theoretical description of the flow dynamics of yield stress materials, emphasizing in particular the role played by relaxation time scales, the interplay between shear flow and aging behavior, the existence of inhomogeneous shear flows and shear bands, wall slip, and non-local effects in confined geometries.
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