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Mechanical properties of disordered materials are governed by their underlying free energy landscape. In contrast to external fields, embedding a small fraction of active particles within a disordered material generates non-equilibrium internal fields, which can help to circumvent kinetic barriers and modulate the free energy landscape. In this work, we investigate through computer simulations how the activity of active particles alters the mechanical response of deeply annealed polydisperse colloidal gels. We show that the 'swim force' generated by the embedded active particles is responsible for determining the mode of mechanical failure, i.e., brittle vs. ductile. We find, and theoretically justify, that at a critical swim force the mechanical properties of the gel decrease abruptly, signaling a change in the mode of mechanical failure. The weakening of the elastic modulus above the critical swim force results from the change in gel porosity and distribution of attractive forces among gel particles. Below the critical swim force, the ductility enhancement is caused by an increase of gel structural disorder. Above the critical swim force, the gel develops a pronounced heterogeneous structure characterized by multiple pore spaces, and the mechanical response is controlled by dynamical heterogeneities. We contrast these results with those of a simulated monodisperse gel that exhibits a non-monotonic trend of ductility modulation with increasing swim force, revealing a complex interplay between the gel energy landscape and embedded activity.

Bacteria can swim upstream due to hydrodynamic interactions with the fluid flow in a narrow tube, and pose a clinical threat of urinary tract infection to patients implanted with catheters. Coatings and structured surfaces have been proposed as a way to suppress bacterial contamination in catheters. However, there is no surface structuring or coating approach to date that thoroughly addresses the contamination problem. Here, based on the physical mechanism of upstream swimming, we propose a novel geometric design, optimized by an AI model predicting in-flow bacterial dynamics. The AI method, based on Fourier neural operator, offers significant speedups over traditional simulation methods. Using Escherichia coli, we demonstrate the anti-infection mechanism in quasi-2D micro-fluidic experiments and evaluate the effectiveness of the design in 3Dprinted prototype catheters under clinical flow rates. Our catheter design shows 1-2 orders of magnitude improved suppression of bacterial contamination at the upstream end of the catheter, potentially prolonging the in-dwelling time for catheter use and reducing the overall risk of catheter-associated urinary tract infections., Comment: maint text 4 figures, SI 5 figures

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 towards a general theory for nonequilibrium phase transitions.

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field, particles rotate to align with the field and accumulate downstream in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement., Comment: 13 pages, 7 figures

In microrheology, the local rheological properties such as viscoelasticity of a complex fluid are inferred from the free or forced motion of embedded colloidal probe particles. Theoretical machinery developed for forced-probe microrheology of colloidal suspensions focused on either constant-force (CF) or constant-velocity (CV) probes while in experiments neither the force nor the kinematics of the probe is fixed. More importantly, the constraint of CF or CV introduces a difficulty in the meaningful quantification of the fluctuations of the probe due to a thermodynamic uncertainty relation. It is known that for a Brownian particle trapped in a harmonic potential well, the product of the standard deviations of the trap force and the particle position is $d k_BT$ in $d$ dimensions with $k_BT$ being the thermal energy. As a result, if the force (position) is not allowed to fluctuate, the position (force) fluctuation becomes infinite. To allow the measurement of fluctuations, in this work we consider a microrheology model in which the embedded probe is dragged along by a moving harmonic potential so that both its position and the trap force are allowed to fluctuate. Starting from the full Smoluchowski equation governing the dynamics of $N$ hard active Brownian particles, we derive a pair Smoluchowski equation describing the dynamics of the probe as it interacts with one bath particle by neglecting hydrodynamic interactions among particles in the dilute limit. From this, we determine the mean and the variance (i.e., fluctuation) of the probe position in terms of the pair probability distribution. We then characterize the behavior of the system in the limits of both weak and strong trap. By taking appropriate limits, we show that our generalized model can be reduced to the well-studied CF or CV microrheology models., Comment: 16 pages, 1 figure

Particle-tracking microrheology of dilute active (self-propelled) colloidal suspensions is studied by considering the external force required to maintain the steady motion of an immersed constant-velocity colloidal probe. If the probe speed is zero, the suspension microstructure is isotropic but exhibits a boundary accumulation of active bath particles at contact due to their self-propulsion. As the probe moves through the suspension, the microstructure is distorted from the nonequilibrium isotropic state, which allows us to define a microviscosity for the suspension using the Stokes drag law. For a slow probe, we show that active suspensions exhibit a swim-thinning behavior in which their microviscosity is gradually lowered from that of passive suspensions as the swim speed increases. When the probe speed is fast, the suspension activity is obscured by the rapid advection of the probe and the measured microviscosity is indistinguishable from that of passive suspensions. Generally for finite activity, the suspension exhibits a velocity-thinning behavior -- though with a zero-velocity plateau lower than passive suspensions -- as a function of the probe speed. These behaviors originate from the interplay between the suspension activity and the hard-sphere excluded-volume interaction between the probe and a bath particle., Comment: 19 pages, 12 figures

Modern biomedical applications such as targeted drug delivery require a delivery system capable of enhanced transport beyond that of passive Brownian diffusion. In this work an osmotic mechanism for the propulsion of a vesicle immersed in a viscous fluid is proposed. By maintaining a steady-state solute gradient inside the vesicle, a seepage flow of the solvent (e.g., water) across the semipermeable membrane is generated which in turn propels the vesicle. We develop a theoretical model for this vesicle-solute system in which the seepage flow is described by a Darcy flow. Using the reciprocal theorem for Stokes flow it is shown that the seepage velocity at the exterior surface of the vesicle generates a thrust force which is balanced by the hydrodynamic drag such that there is no net force on the vesicle. We characterize the motility of the vesicle in relation to the concentration distribution of the solute confined inside the vesicle. Any osmotic solute is able to propel the vesicle so long as a concentration gradient is present. In the present work, we propose active Brownian particles (ABPs) as a solute. To maintain a symmetry-breaking concentration gradient, we consider ABPs with spatially varying swim speed and ABPs with constant properties but under the influence of an orienting field. In particular, it is shown that at high activity the vesicle velocity is $\boldsymbol{U}\sim [K_\perp /(\eta_e\ell_m) ]\int \Pi_0^\mathrm{swim} \boldsymbol{n} d\Omega $, where $\Pi_0^\mathrm{swim}$ is the swim pressure just outside the thin accumulation boundary layer on the interior vesicle surface, $\boldsymbol{n}$ is the unit normal vector of the vesicle boundary, $K_\perp$ is the membrane permeability, $\eta_e$ is the viscosity of the solvent, and $\ell_m$ is the membrane thickness.

Control of self-propelled particles is central to the development of many microrobotic technologies, from dynamically reconfigurable materials to advanced lab-on-a-chip systems. However, there are few physical principles by which particle trajectories can be specified and can be used to generate a wide range of behaviors. Within the field of ray optics, a single principle for controlling the trajectory of light -- Snell's law -- yields an intuitive framework for engineering a broad range of devices, from microscopes to cameras and telescopes. Here we show that the motion of self-propelled particles gliding across a resistance discontinuity is governed by a variant of Snell's law, and develop a corresponding ray optics for gliders. Just as the ratio of refractive indexes sets the path of a light ray, the ratio of resistance coefficients is shown to determine the trajectories of gliders. The magnitude of refraction depends on the glider's shape, in particular its aspect ratio, which serves as an analog to the wavelength of light. This enables the demixing of a polymorphic, many-shaped, beam of gliders into distinct monomorphic, single-shaped, beams through a friction prism. In turn, beams of monomorphic gliders can be focused by spherical and gradient friction lenses. Alternatively, the critical angle for total internal reflection can be used to create shape-selective glider traps. Overall our work suggests that furthering the analogy between light and microscopic gliders will result in a wide range of new devices for sorting, concentrating, and analyzing self-propelled particles.

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.

Since its development, Stokesian Dynamics has been a leading approach for the dynamic simulation of suspensions of particles at arbitrary concentrations with full hydrodynamic interactions. Although originally developed for the simulation of passive particle suspensions, the Stokesian Dynamics framework is equally well suited to the analysis and dynamic simulation of suspensions of active particles, as we elucidate here. We show how the reciprocal theorem can be used to formulate the exact dynamics for a suspension of arbitrary active particles and then show how the Stokesian Dynamics method provides a rigorous way to approximate and compute the dynamics of dense active suspensions where many-body hydrodynamic interactions are important., Comment: 16 pages, 3 figures

Many active matter systems are known to perform L\'{e}vy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been observed for microswimmers such as bacteria in microfluidic experiments, where Gaussian noise assumptions are insufficient to explain the data. We introduce \textit{active L\'evy swimmers} to model such behavior. The focus is on ideal swimmers that only interact with the walls but not with each other, which reduces to the classical L\'evy walk model but now under confinement. We study the density distribution in the channel and force exerted on the walls by the L\'evy swimmers, where the boundaries require proper explicit treatment. We analyze stronger confinement via a set of coupled kinetics equations and the swimmers' stochastic trajectories. Previous literature demonstrated that power-law scaling in a multiscale analysis in free space results in a fractional diffusion equation. We show that in a channel, in the weak confinement limit active L\'evy swimmers are governed by a modified Riesz fractional derivative. Leveraging recent results on fractional fluxes, we derive steady state solutions for the bulk density distribution of active L\'evy swimmers in a channel, and demonstrate that these solutions agree well with particle simulations. The profiles are non-uniform over the entire domain, in contrast to constant-in-the-bulk profiles of active Brownian and run-and-tumble particles. Our theory provides a mathematical framework for L\'evy walks under confinement with sliding no-flux boundary conditions and provides a foundation for studies of interacting active L\'evy swimmers., Comment: 25 pages, 4 figures

We demonstrate that deep learning techniques can be used to predict motility induced phase separation (MIPS) in suspensions of active Brownian particles (ABPs) by creating a notion of phase at the particle level. Using a fully connected network in conjunction with a graph neural network we use individual particle features to predict to which phase a particle belongs. From this, we are able to compute the fraction of dilute particles to determine if the system is in the homogeneous dilute, dense, or coexistence region. Our predictions are compared against the MIPS binodal computed from simulation. The strong agreement between the two suggests that machine learning provides an effective way to determine the phase behavior of ABPs and could prove useful for determining more complex phase diagrams.

We demonstrate that the mechanically-defined "isothermal" compressibility behaves as a thermodynamic-like response function for suspensions of active Brownian particles. The compressibility computed from the active pressure - a combination of the collision and unique swim pressures - is capable of predicting the critical point for motility induced phase separation, as expected from the mechanical stability criterion. We relate this mechanical definition to the static structure factor via an active form of the thermodynamic compressibility equation and find the two to be equivalent, as would be the case for equilibrium systems. This equivalence indicates that compressibility behaves like a thermodynamic response function, even when activity is large. Finally, we discuss the importance of the phase interface when defining an active chemical potential. Previous definitions of the active chemical potential are shown to be accurate above the critical point but breakdown in the coexistence region. Inclusion of the swim pressure in the mechanical compressibility definition suggests that the interface is essential for determining phase behavior.

By introducing the notion of a dynamic overlap concentration scale, we identify universal and previously unreported features of the mechanical properties of active colloids. These features are codified by recognizing that the characteristic length scale of an active particle's trajectory, the run-length, introduces a new concentration scale $\phi^*$. Large-scale simulations of repulsive active Brownian particles (ABPs) confirm that this new run-length dependent concentration, which is the trajectory-space analogue of the overlap concentration in polymer solutions, delineates distinct concentration regimes in which interparticle collisions alter particle trajectories. Using $\phi^*$ and concentration scales associated with colloidal jamming, the mechanical equation-of-state for ABPs can be collapsed onto a set of principal curves that contain a number of previously 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 be of great utility in unraveling the behavior of active and driven systems.

The unique pressure exerted by active particles -- the "swim" pressure -- has proven to be a useful quantity in explaining many of the seemingly confounding behaviors of active particles. However, its use has also resulted in some puzzling findings including an \textit{extremely negative} surface tension between phase separated active particles. Here, we demonstrate that this contradiction stems from the fact that the swim pressure \textit{is not a true pressure}. At a boundary or interface, the reduction in particle swimming generates a net active force density -- an entirely \textit{self-generated body force}. The pressure at the boundary, which was previously identified as the swim pressure, is in fact an elevated (relative to the bulk) value of the \textit{traditional particle pressure} that is generated by this interfacial force density. Recognizing this unique mechanism for stress generation allows us to define a much more physically plausible surface tension. We clarify the utility of the swim pressure as an "equivalent pressure" (analogous to those defined from electrostatic and gravitational body forces) and the conditions in which this concept can be appropriately applied., Comment: Submitted June 6, 2019; to appear in Physical Review E. Main text with appendices (8 pages, 6 figures) and Supplemental Material (2 pages, 1 figure). Supplemental videos available upon request or at https://drive.google.com/drive/folders/14Isyut7SRvyrb8PfTwucVcZIPhonh8Ax?usp=sharing

External fields can decidedly alter the free energy landscape of soft materials and can be exploited as a powerful tool for the assembly of targeted nanostructures and colloidal materials. Here, we use computer simulations to demonstrate that nonequilibrium internal fields or forces -- forces that are generated by driven components within a system -- in the form of active particles can precisely modulate the dynamical free energy landscape of a model soft material, a colloidal gel. Embedding a small fraction of active particles within a gel can provide a unique pathway for the dynamically frustrated network to circumvent the kinetic barriers associated with reaching a lower free energy state through thermal fluctuations alone. Moreover, by carefully tuning the active particle properties (the propulsive swim force and persistence length) in comparison to those of the gel, the active particles may induce depletion-like forces between the constituent particles of the gel despite there being no geometric size asymmetry between the particles. These resulting forces can rapidly push the system toward disparate regions of phase space. Intriguingly, the state of the material can be altered by tuning macroscopic transport properties such as the solvent viscosity. Our findings highlight the potential wide-ranging structural and kinetic control facilitated by varying the dynamical properties of a remarkably small fraction of driven particles embedded in a host material., Comment: ACS Nano

Active Brownian Particles (ABPs) transmit a swim pressure $\Pi^{swim}=n\zeta D^{swim}$ to the container boundaries, where $\zeta$ is the drag coefficient, $D^{swim}$ is the swim diffusivity and $n$ is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress $\mathbf{\sigma}^{swim} = - n \zeta \mathbf{D}^{swim}$, which is related to the anisotropic swim diffusivity $\mathbf{D}^{swim}$. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems, and the anisotropy is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure $\Pi^{swim}=-(\mathbf{\sigma}^{swim}\cdot\mathbf{n})\cdot\mathbf{n}$ on a wall with normal vector $\mathbf{n}$, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components -- the normal stress difference -- generates a net flow of ABPs along the wall, which is a generic property of active matter systems.

The finite reorient-time of swimmers leads to a finite run length $\ell$ and the kinetic accumulation boundary layer on the microscopic length scale $\delta$ on a non-penetrating wall. That boundary layer is the microscopic origin of the swim pressure, and is impacted by the geometry of the boundary [Yan \& Brady, \textit{J. Fluid. Mech.}, 2015, \textbf{785}, R1]. In this work we extend the analysis to analytically solve the boundary layer on an arbitrary-shaped body distorted by the local mean curvature. The solution gives the swim pressure distribution and the total force (torque) on an arbitrarily shaped body immersed in swimmers, with a general scaling of the curvature effect $\Pi^{swim}\sim\lambda\delta^2/L$.

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a `chemical' coupling parameter $\Gamma_c$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic One Component Plasma (OCP) system. When confined to a constant-volume domain, Body-Centered Cubic crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-Centered Cubic crystals may also be stable. The `melting point' of the `liquid-to-crystal transition' occurs at $\Gamma_c\approx140$ for both BCC and FCC lattices.

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.

We study the diffusion of a Brownian probe particle of size $R$ in a dilute dispersion of active Brownian particles (ABPs) of size $a$, characteristic swim speed $U_0$, reorientation time $\tau_R$, and mechanical energy $k_s T_s = \zeta_a U_0^2 \tau_R /6$, where $\zeta_a$ is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity $D_P = k_B T/\zeta_P$, where $k_B T$ is the thermal energy of the solvent and $\zeta_P$ is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by $Pe_s = U_0 a /D_P$. The active contribution to the diffusivity scales as $Pe_s^2$ for weak swimming and $Pe_s$ for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale $\tau_R$, the active diffusivity scales as $k_s T_s /\zeta_P$: the probe moves as if it were immersed in a solvent with energy $k_s T_s$ rather than $k_B T$., Comment: 5 pages, 3 figures, submitted for publication. Please contact authors regarding supplemental information

This is a reply to the recent comment from Ikeda, Berthier, and Sollich (arXiv:1602.04796) on "Constant stress and pressure rheology of colloidal suspensions", Phys. Rev. Lett. 115, 158301 (2015)., Comment: 2 pages, 1 figure

Hard sphere colloidal particles are a basic model system for general research into phase behavior, ordering and out-equilibrium glass transitions. Experimentally it has been shown that oscillatory shearing of a monodisperse hard sphere glass, produces two different crystal orientations; a Face Centered Cubic (FCC) crystal with the close packed direction parallel to shear at high strains and an FCC crystal with the close packed direction perpendicular to shear at low strains. Here, using Brownian dynamics simulations of hard sphere particles, we have examined high volume fraction shear-induced crystals under oscillatory shear as well as the same volume fraction glass counterparts. We find that, while the displacements under shear of the glass are isotropic, the sheared FCC crystal structures oriented parallel to shear, are anisotropic due to the cooperative motion of velocity-vorticity layers of particles sliding over each other. These sliding layers generally result in lower stresses and less overall particle displacements. Additionally, from the two crystal types, the perpendicular crystal exhibits less stresses and displacements at smaller strains, however at larger strains, the sliding layers of the parallel crystal are found to be more efficient in minimizing stresses and displacements, while the perpendicular crystal becomes unstable. The findings of this work suggest that the process of shear-induced ordering for a colloidal glass is facilitated by large out of cage displacements, which allow the system to explore the energy landscape and find the minima in energy, stresses and displacements by configuring particles into a crystal oriented parallel to shear.

We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy $k_BT$ to the swimmer's activity $k_sT_s = \zeta U_0^2\tau_R/6$, where $\zeta$ is the Stokes drag coefficient, $U_0$ is the swim speed and $\tau_R$ is the reorientation time of the active particles. The theory has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behavior when the boundary size is large compared to the swimmer's run length $\ell = U_0\tau_R$. The theory is used to predict the motion of bodies of all sizes immersed in active matter., Comment: JFM Rapids

In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J. Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118 (2003) 10323]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall $\mathcal{O}(N\log N)$ computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions., Comment: 39 pages, 21 figures

We introduce fractal liquids by generalizing classical liquids of integer dimensions $d = 1, 2, 3$ to a fractal dimension $d_f$. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined to a fractal polymer backbone in a gel. Here we study the thermodynamics and pair correlations of fractal liquids by computer simulation and semi-analytical statistical mechanics. Our results are based on a model where fractal hard spheres move on a near-critical percolating lattice cluster. The predictions of the fractal Percus-Yevick liquid integral equation compare well with our simulation results., Comment: Changed title

We present a comprehensive computational study of the short-time transport properties of bidisperse neutral colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to $4$, and total volume fractions up to and beyond the monodisperse hard-sphere close packing limit. The many-body hydrodynamic interactions are computed using conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address suspension properties including the short-time translational and rotational self-diffusivities, the instantaneous sedimentation velocity, the wavenumber-dependent partial hydrodynamic functions, and the high-frequency shear and bulk viscosities; and porous media properties including the permeability and the translational and rotational hindered diffusivities. We carefully compare the SD computations with existing theoretical and numerical results. For suspensions, we also explore the range of validity of various approximation schemes, notably the Pairwise Additive (PA) approximations with the Percus-Yevick structural input. We critically assess the strengths and weaknesses of the SD algorithm for various transport properties. For very dense systems, we discuss in detail the interplay between the hydrodynamic interactions and the structures due to the presence of a second species of a different size., Comment: 26 pages, 26 figures

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 figures

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's $\delta\gamma$-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified $\delta\gamma$ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as $40\%$., Comment: 12 pages, 6 figures