Van't Hoff's law for active suspensions: the role of the solvent chemical potential

Concentration Dependence of Elastic and Viscoelastic Properties of Aqueous Solutions of Ficoll and Bovine Serum Albumin by Brillouin Light Scattering Spectroscopy

The cellular environment is crowded with macromolecules of different shapes and sizes. The effect of this macromolecular crowding has been studied in a variety of synthetic crowding environments: two popular examples are the compact colloid-like Ficoll macromolecule and the globular protein bovine serum albumin (BSA). Recent studies have indicated that a significant component of bound or surface-associated water in these crowders reduces the available free volume. In this work, Brillouin light scattering experiments were performed on aqueous solutions of Ficoll 70 and Ficoll 400 with concentrations ranging from 1 to 35 wt % and BSA with concentrations of 1 to 27 wt %. From the dependence of spectral peak parameters on polymer concentration, we determined fundamental solution properties: hypersound velocity, adiabatic bulk modulus and compressibility, apparent viscosity, and hypersound attenuation. The existing theory that ignores intermolecular interactions can capture only the observed linear trends in the frequency shift up to a threshold concentration, beyond which a quadratic term accounting for intermolecular interactions is necessary. This likely indicates a transition from the dilute to semidilute regime. In the Ficoll solutions (but not BSA), we see evidence for a central mode, which is indicative of relaxation in the hydration shell of Ficoll.

Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Thermoresponsive Ionic Liquid with Different Cation-Anion Pairs as Draw Solutes in Forward Osmosis

We synthesized various phosphonium- and ammonium-based ionic liquids (ILs), using benzenesulfonate (BS) and 4-methylbenzenesulfonate (MBS) to establish the criteria for designing an ideal draw solute in a forward osmosis (FO) system. Additionally, the effects of monocationic, dicationic, and anionic species on FO performance were studied. Monocationic compounds ([P₄₄₄₄][BS], [P₄₄₄₄][MBS], [N₄₄₄₄][BS], and [N₄₄₄₄][MBS]) were obtained in one step via anion exchange. Dicationic compounds ([(P₄₄₄₄)₂][BS], [(P₄₄₄₄)₂][MBS], [(N₄₄₄₄)₂][BS], and [(N₄₄₄₄)₂][MBS]) were prepared in two steps via a Menshutkin SN₂ reaction and anion exchange. We also investigated the suitability of ILs as draw solutes for FO systems. The aqueous [P₄₄₄₄][BS], [N₄₄₄₄][BS], [N₄₄₄₄][MBS], and [(N₄₄₄₄)₂][BS] solutions did not exhibit thermoresponsive behavior. However, 20 wt% [P₄₄₄₄][MBS], [(P₄₄₄₄)₂][BS], [(P₄₄₄₄)₂][MBS], and [(N₄₄₄₄)₂][MBS] had critical temperatures of approximately 43, 33, 22, and 60 °C, respectively, enabling their recovery using temperature. An increase in IL hydrophobicity and bulkiness reduces its miscibility with water, demonstrating that it can be used to tune its thermoresponsive properties. Moreover, the FO performance of 20 wt% aqueous [(P₄₄₄₄)₂][MBS] solution was tested for water flux and found to be approximately 10.58 LMH with the active layer facing the draw solution mode and 9.40 LMH with the active layer facing the feed solution.

Dynamic overlap concentration scale of active colloids

By introducing the notion of a dynamic overlap concentration scale, we identify additional universal features of the mechanical properties of active colloids. We codify these features by recognizing that the characteristic length scale of an active particle's trajectory, the run length, introduces a concentration scale ϕ^{*}. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this run-length dependent concentration, the trajectory-space analog of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using ϕ^{*} and concentration scales associated with colloidal jamming, the mechanical equation of state for ABPs collapses onto a set of principal curves that contain several overlooked features. The inclusion of these features qualitatively alters previous predictions of the behavior for active colloids, as we demonstrate by computing the spinodal for a suspension of purely repulsive ABPs. Our findings suggest that dynamic overlap concentration scales should help unravel the behavior of active and driven systems.

Osmotic evolution of composite liquid marbles

HYPOTHESIS

We hypothesized that the reported evolution (growth) of composite water marbles filled with saline water and coated with lycopodium dispersed in a thin layer of silicone oil is due to the osmotic mass transfer. The hypothesis is supported by the semi-empirical model of osmotic growth of small liquid marbles floating on distilled water.

EXPERIMENTS

Saline composite, silicone oil-coated marbles floating on distilled water grew with time; whereas, composite marbles filled with distilled water floating on aqueous solutions of NaCl lost mass with time and shrunk. However, composite liquid marbles filled with saline water and floating on aqueous solutions of NaCl remained stable during 25 h of the laboratory experiment.

FINDINGS

The reported findings are reasonably attributed to osmotic mass transport through the thin silicon layer filled with lycopodium particles coating the marbles, acting as an osmotic membrane. This is supported by the suggested model for the osmotic growth of marbles.

Motility-induced inter-particle correlations and dynamics: a microscopic approach for active Brownian particles

Amongst the theoretical approaches towards the dynamics and phase behaviour of suspensions of active Brownian particles (ABPs), no attempt has been made to specify the motility-induced inter-particle correlations as quantified by the pair-correlation function. Here, we derive expressions for the pair-correlation function for ABPs with very short-ranged direct interactions for small and large swimming velocities and low concentrations. The pair-correlation function is the solution of a differential equation that is obtained from the Fokker-Planck equation for the probability density function of the positions and orientations of the ABPs. For large swimming Peclet numbers, λ, the pair-correlation function is highly asymmetric. The pair-correlation function attains a large value, ∼λ, within a small region of spatial extent, ∼1/λ, near contact of the ABPs when the ABPs approach each other. The pair-correlation function is small within a large region of spatial extent, ∼λ1/3, when the ABPs move apart, with a contact value that is essentially zero. From the explicit expressions for the pair-correlation function, Fick's diffusion equation is generalized to include motility. It is shown that mass transport, in case of large swimming velocities, is dominated by a preferred swimming direction that is induced by concentration gradients. The expression for the pair-correlation function derived in this paper could serve as a starting point to obtain approximate results for high concentrations, which could then be employed in a first-principles analysis of the dynamics and phase behaviour of ABPs at higher concentrations.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Surface Tensions between Active Fluids and Solid Interfaces: Bare vs Dressed

We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial forces are of a more complex nature. Using a number of macroscopic setups, we show that the surface tension is a combination of an equation-of-state abiding part and of setup-dependent contributions. The latter arise from generic setup-dependent steady currents which "dress" the measurement of the "bare" surface tension. The former shares interesting properties with its equilibrium counterpart, and can be used to generalize the Young-Laplace law to active systems. Finally, we show how a suitably designed probe can directly access this bare surface tension, which can also be computed using a generalized virial formula.

Resonant osmosis across active switchable membranes

To overcome the traditional paradigm of filtration, where separation is essentially performed upon steric sieving principles, we explore the concept of dynamic osmosis through active membranes. A partially permeable membrane presents a time-tuneable feature that changes the effective pore interaction with the solute and thus actively changes permeability with time. In general, we find that slow flickering frequencies effectively decrease the osmotic pressure and large flickering frequencies do not change it. In the presence of an asymmetric membrane, we find a resonant frequency where pumping of the solute is performed and can be analyzed in terms of ratchet transport. We discuss and highlight the properties of this resonant osmotic transport. Furthermore, we show that dynamic osmosis allows us to pump the solute at the nanoscale using less energy than reverse osmosis. This opens new possibilities to build advanced filtration devices and design artificial ionic machinery.

Breakdown of effective temperature, power law interactions, and self-propulsion in a momentum-conserving active fluid

The simplest extensions of single-particle dynamics in a momentum-conserving active fluid-an active suspension of two colloidal particles or a single particle confined by a wall-exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero-entropy production rate. This is a consequence of hydrodynamic interactions that introduce multiplicative noise in the stochastic description of particle positions. This results in fluctuation-induced interactions that depend on distance as a power law. We find that the dynamics of activated colloids in a passive fluid, with stochastic forcing localized on the particle, is different from that of passive colloids in an active fluctuating fluid.

Scalar activity induced phase separation and liquid-solid transition in a Lennard-Jones system

We report scalar activity induced phase separation and crystallization in a system of 3-d Lennard-Jones particles taken at state points spanning from the gas to the liquid regime using molecular dynamics simulation (MD). Scalar activity was introduced by increasing the temperature of half of the particles (labeled 'hot') while keeping the temperature of the other half constant at a lower value (labeled 'cold'). The relative temperature difference between the two subsystems is considered as a measure of the activity. From our simulations we observe that the two species tend to phase separate at sufficiently high activity ratio. The extent of separation is quantified by the defined order parameter and the entropy production during this process is determined by employing the two-phase thermodynamic (2PT) model and the standard modified Benedict-Webb-Rubin (MBWR) equation of state for a LJ fluid. We observe that the extent of the phase separation and entropy production increases with the density of the system. From a cluster analysis, we obtain the mean number of clusters ncl, and the mean size of the largest cluster n0 in the system, complementing each other. Bond orientation order parameters reveal that the so formed largest cluster also develops solid-like order consisting of both FCC and HCP packing. The presence of such crystalline order is also supported by a common neighbor analysis.

Particle motion driven by non-uniform thermodynamic forces

We present a complete reciprocal description of particle motion inside multi-component fluids that extends the conventional Onsager formulation of non-equilibrium transport to systems where the thermodynamic forces are non-uniform on the colloidal scale. Based on the dynamic length and time scale separation in suspensions, the particle flux is shown to be related to the volume-averaged coupling between the Stokes flow tensor and the thermodynamic force density acting on the fluid. The flux is then expressed in terms of thermodynamic quantities that can be computed from the interfacial properties and equation of state of the colloids. Our results correctly describe diffusion and sedimentation and suggest that force-free phoretic motion can occur even in the absence of interfacial interactions, provided that the thermodynamic gradients are non-uniform at the colloidal surface. In particular, we derive an explicit hydrodynamic form for the phoretic force resulting from these non-uniform gradients. The form is validated by the recovery of the Henry function for electrophoresis and the Ruckenstein term for thermophoresis.

Osmosis, from molecular insights to large-scale applications

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.

Active particles under confinement and effective force generation among surfaces

We consider the effect of geometric confinement on the steady-state properties of a one-dimensional active suspension subject to thermal noise. The random active force is modeled by an Ornstein-Uhlenbeck process and the system is studied both numerically, by integrating the Langevin governing equations, and analytically by solving the associated Fokker-Planck equation under suitable approximations. The comparison between the two approaches displays a fairly good agreement and in particular, we show that the Fokker-Planck approach can predict the structure of the system both in the wall region and in the bulk-like region where the surface forces are negligible. The simultaneous presence of thermal noise and active forces determines the formation of a layer, extending from the walls towards the bulk, where the system exhibits polar order. We relate the presence of such ordering to the mechanical pressure exerted on the container's walls and show how it depends on the separation of the boundaries and determines a Casimir-like attractive force mediated by the active suspension.

Active ideal sedimentation: exact two-dimensional steady states

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.