Theory for the Casimir effect and the partitioning of active matter

On Casimir and Helmholtz Fluctuation-Induced Forces in Micro- and Nano-Systems: Survey of Some Basic Results

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.

AI-aided geometric design of anti-infection catheters

Bacteria can swim upstream 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 to repel bacteria, but no such approach thoroughly addresses the contamination problem in catheters. Here, on the basis of the physical mechanism of upstream swimming, we propose a novel geometric design, optimized by an artificial intelligence model. Using Escherichia coli, we demonstrate the anti-infection mechanism in microfluidic experiments and evaluate the effectiveness of the design in three-dimensionally printed prototype catheters under clinical flow rates. Our catheter design shows that one to two orders of magnitude improved suppression of bacterial contamination at the upstream end, potentially prolonging the in-dwelling time for catheter use and reducing the overall risk of catheter-associated urinary tract infection.

Active depletion torque between two passive rods

The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.

Partitioning of active particles into porous media

Passive Brownian particles partition homogeneously between a porous medium and an adjacent fluid reservoir. In contrast, active particles accumulate near boundaries and can therefore preferentially partition into the porous medium. Understanding how active particles interact with and partition into such an environment is important for optimizing particle transport. In this work, both the initial transient and steady behavior as active swimmers partition into a porous medium from a bulk fluid reservoir are investigated. At short times, the particle number density in the porous medium exhibits an oscillatory behavior due to the particles' ballistic motion when time t < τ_R, where τ_R is the reorientation time of the active particles. At longer times, t > L²/D^swim, the particles diffuse from the reservoir into the porous medium, leading to a steady state concentration partitioning. Here, L is the characteristic length scale of the porous medium and D^swim = U₀/d(d - 1), where U₀ is the intrinsic swim speed of the particles,  = U₀τ_R is the particles' run, or persistence, length, and d is the dimension of the reorientation process. An analytical prediction is developed for this partitioning for spherical obstacles connected to a fluid reservoir in both two and three dimensions based on the Smoluchowski equation and a macroscopic mechanical momentum balance. The analytical prediction agrees well with Brownian dynamics simulations.

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

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.