arXiv subjects

John F. Brady

Publications and source records attributed to John F. Brady.

At least 19 recordsLinked to original sources

arXiv2026

Reviving the Suspension Balance Model

The Suspension Balance Model (SBM) [J. Fluid Mech. \textbf{275}, 157 (1994)] for two-phase flows uses the momentum balance of the particle phase as a closure for the particle flux, showing that particle migration is driven by the divergence of the particle-phase stress. The underlying basis of this model was challenged by Nott~et~al.\ [Phys. Fluids \textbf{23}, 043304 (2011)] where the authors argued that the hydrodynamic contributions to the suspension stress should not appear in the particle-phase momentum balance, being replaced by a different particle-phase stress. The particle-phase stress proposed by Nott~et~al., while mathematically correct, involves the partitioning of the (non-pairwise-additive) hydrodynamic forces, and care is needed to understand how the force on a chosen particle is affected by a second particle. We show by a simple two-particle calculation what is the proper partitioning, and show that it is consistent thermodynamically and gives the correct equilibrium osmotic pressure of Brownian colloids. Using Stokesian Dyanmics suspension rheology, we quantitatively demonstrate that the hydrodynamic contribution to the suspension stress is virtually identical to particle-phase stress; the only difference is that the isolated single-particle hydrodynamic stress contribution -- the Einstein viscosity correction -- must be removed from the suspension stress when used to predict particle flux. Our results validate a key assumption of the SBM and therefore revive its physical foundation.

physics.flu-dyn↗

arXiv2025

Nonmonotonic diffusion in sheared active suspensions of squirmers

We investigate how shear influences the dynamics of active particles in dilute to concentrated suspensions. Using apolar active suspensions of squirmers as model systems, we show how their long-time diffusive dynamics can surprisingly slow down and vary nonmonotonically with the shear rate arising from an interplay between the activity-induced persistent motion and shear-induced reorientation and diffusion. Further simulations of self-propelled particles with tunable persistence exhibit richer dynamics and confirm the observed coupling, suggesting that nonmonotonic diffusion may be a general feature of fluids endowed with an underlying microstructure and large persistence. Our results reveal a nonlinear effect of shear on diffusion in active suspensions, elucidate how internal and external forcing interact, and provide new possibilities to modulate transport in active fluids.

cond-mat.soft↗

arXiv2025

Hydrodynamic interactions destroy motility-induced phase separation in active suspensions

Motility-Induced Phase Separation (MIPS) is a distinctive phenomenon in active matter that arises from its inherent non-equilibrium nature. Despite recent progress in understanding MIPS in dry active systems, it has been debated whether MIPS can be observed in wet systems in which fluid-mediated hydrodynamic interactions (HI) are present. We use theory and large-scale {\it Active Fast Stokesian Dynamics} simulations of the so-called squirmer model to show that collision-induced pusher force dipoles, which are present even for the simplest neutral squirmers (stealth swimmers), destroy MIPS when HI are included. Both rotational and translational HI independently suppress phase separation: rotation by shortening a swimmer's persistence length (and thus reducing the swim pressure), translation by a confinement-scale advective fluid flow. We further clarify that collisional dipoles between swimmers and boundaries can generate attractive flows that promote particle aggregation observed in some previous simulations and experiments. Finally, we show how to recover MIPS in fluidic environments by tuning the magnitude of the HI through brush-like surface coatings on the active particles.

cond-mat.soft↗

arXiv2024

Active doping controls the mode of failure in dense colloidal gels

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.

cond-mat.soft↗

arXiv2023

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 towards a general theory for nonequilibrium phase transitions.

cond-mat.stat-mech↗

arXiv2023

AI-aided Geometric Design of Anti-infection Catheters

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.

physics.med-ph↗

arXiv2023

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.

cond-mat.soft↗

arXiv2022

Confined active matter in external fields

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.

cond-mat.soft↗

arXiv2022

Forced microrheology of active colloids

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.

cond-mat.soft↗

arXiv2022

Trapped-particle microrheology of active suspensions

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.

cond-mat.soft↗

arXiv2022

Ray Optics for Gliders

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.

cond-mat.soft↗

arXiv2022

Activity-induced propulsion of a vesicle

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 $\boldsymbol{U}\sim [K_\perp /(η_e\ell_m) ]\int Π_0^\mathrm{swim} \boldsymbol{n} dΩ$, where $Π_0^\mathrm{swim}$ 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, $η_e$ is the viscosity of the solvent, and $\ell_m$ is the membrane thickness.

physics.flu-dyn↗

arXiv2021

Active Stokesian Dynamics

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.

physics.flu-dyn↗

arXiv2021

Distribution and pressure of active Lévy swimmers under confinement

Many active matter systems are known to perform Lévy 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 Lévy 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 Lévy walk model but now under confinement. We study the density distribution in the channel and force exerted on the walls by the Lévy 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 Lévy 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 Lévy 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 Lévy walks under confinement with sliding no-flux boundary conditions and provides a foundation for studies of interacting active Lévy swimmers.

cond-mat.soft↗

arXiv2020

Machine Learning for Phase Behavior in Active Matter Systems

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.

cond-mat.soft↗

arXiv2020

The "isothermal" compressibility of active matter

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.

cond-mat.soft↗

arXiv2020

Dynamic Overlap Concentration Scale of Active Colloids

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 $ϕ^*$. 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 $ϕ^*$ 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.

cond-mat.soft↗

arXiv2019

Microscopic Origins of the Swim Pressure and the Anomalous Surface Tension of Active Matter

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.

cond-mat.soft↗