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Transport and dispersion of active particles in structured environments such as corrugated channels and porous media are important for the understanding of both natural and engineered active systems. Owing to their continuous self-propulsion, active particles exhibit rectified transport under spatially asymmetric confinement. While progress has been made in experiments and particle-based simulations, a theoretical understanding of the effective long-time transport dynamics in spatially periodic geometries remains less developed. In this paper, we apply generalized Taylor dispersion theory (GTDT) to analyze the long-time effective transport dynamics of active Brownian particles (ABPs) in periodic channels and fields. We show that the long-time transport behavior is governed by an effective advection-diffusion equation. The derived macrotransport equations allow us to characterize the average drift and effective dispersion coefficient. For the case of ABPs subject to a no-flux boundary condition at the channel wall, we show that regardless of activity, the average drift is given by the net diffusive flux along the channel. For ABPs, their activity is the driving mechanism that sustains a density gradient, which ultimately leads to rectified motion along the channel. Our continuum theory is validated against direct Brownian dynamics simulations of the Langevin equations governing the motion of each ABP., Comment: 15 pages, 4 figures

Monolayer WSe$_2$ (ML WSe$_2$) exhibits a high second-harmonic generation (SHG) efficiency under single 1-photon (1-p) or 2-photon (2-p) resonant excitation conditions due to enhanced second-order susceptibility compared with off-resonance excitation states \cite{lin2021narrow,wang2015giant}. Here, we propose a novel strain engineering approach to dramatically boost the in-plane second-order nonlinear susceptibility ($\chi_{yyy}$ ) of ML WSe$_2$ by tuning the biaxial strain to shift two K-valley excitons (the A-exciton and a high-lying exciton (HX)) into double resonance. We first identify the A-exciton and HX from the 2D Mott-Wannier model for pristine ML WSe$_2$ and calculate the $\chi_{yyy}$ under either 1-p or 2-p resonance excitations, and observe a $\sim$ 39-fold $\chi_{yyy}$ enhancement arising from the 2-p HX resonance state compared with the A-exciton case. By applying a small uniform biaxial strain (0.16\%), we observe an exciton double resonance state ($E_{\rm{HX}}$ = 2$E_{\rm{A}}$, $E_{\rm{HX}}$ and $E_{\rm{A}}$ are the exciton absorption energies), which yields up to an additional 52-fold enhancement in $\chi_{yyy}$ compared to the 2-p HX resonance state, indicating an overall $\sim$ 2000-fold enhancement compared to the single 2-p A-exciton resonance state reported in Ref \cite{wang2015giant}. Further exploration of the strain-engineered exciton states (with biaxial strain around 0.16\%) reveals that double resonance also occurs at other wavevectors near the K valley, leading to other enhancement states in $\chi_{yyy}$, confirming that strain engineering is an effective approach for enhancing $\chi_{yyy}$. Our findings suggest new avenues for strain engineering the optical properties of 2D materials for novel nonlinear optoelectronic applications.

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work, we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection-diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly-spherical particles, weak flow, and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures., Comment: 15 pages, 14 figures

Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive Brownian particles, the MFPT of ABPs is much less developed. In this paper, we study the MFPT for ABPs in a 1-D domain with absorbing boundary conditions at both ends of the domain. To reveal the effect of swimming on the MFPT, we consider an asymptotic analysis in the weak-swimming or small P\'eclet (Pe) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to O(Pe$^2$). We explore the effects of the starting positions and starting orientations on the MFPT. Our analysis shows that if the starting orientations are biased towards one side of the domain, the MFPT as a function of the starting position becomes asymmetric about the center of the domain. The analytical results were confirmed by the numerical solutions of the full PDE model.

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

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.

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