Sedimentation, trapping, and rectification of dilute bacteria

The run-and-tumble dynamics of bacteria, as exhibited by \textit{E. coli}, offers a simple experimental realization of non-Brownian, yet diffusive, particles. Here we present some analytic and numerical results for models of the ideal (low-density) limit in which the particles have no hydrodynamic or other interactions and hence undergo independent motions. We address three cases: sedimentation under gravity; confinement by a harmonic external potential; and rectification by a strip of `funnel gates' which we model by a zone in which tumble rate depends on swim direction. We compare our results with recent experimental and simulation literature and highlight similarities and differences with the diffusive motion of colloidal particles

Shock wave focusing using geometrical shock dynamics

A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The numerical results exhibit the qualitative behavior of strong, moderate, and weak shock focusing observed experimentally. The physical mechanisms that are influenced by aperture angle and shock strength are properly represented by geometrical shock dynamics. Comparison with experimental measurements of the location at which maximum shock pressure occurs shows good agreement, but the maximum pressure at focus is overestimated by about 60%. This error, though large, is acceptable when the speed and low cost of the method is taken into consideration. The error is primarily due to the under prediction of disturbance speed on weak shock fronts. Adequate resolution of the focal region proves to be particularly important to properly judge the validity of shock dynamics theory, under-resolution leading to overly optimistic conclusions

Computational confirmation of scaling predictions for equilibrium polymers

We report the results of extensive Dynamic Monte Carlo simulations of systems of self-assembled Equilibrium Polymers without rings in good solvent. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav = \Lstar (\phi/\phistar)^\alpha \propto \phi^\alpha \exp(\delta E) with exponents $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = [1+(\gamma-1)/(\nu d -1)]/2 \approx 0.60, \delta_s=1/2$ in the dilute and semi-dilute limits respectively. The average size of the micelles, as measured by the end-to-end distance and the radius of gyration, follows a very similar crossover scaling to that of conventional quenched polymer chains. In the semi-dilute regime, the chain size distribution is found to be exponential, crossing over to a Schultz-Zimm type distribution in the dilute limit. The very large size of our simulations (which involve mean chain lengths up to 5000, even at high polymer densities) allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma = 1.165 \pm 0.01$.Comment: 6 pages, 4 figures, LATE

Two-state shear diagrams for complex fluids in shear flow

The possible "phase diagrams'' for shear-induced phase transitions between two phases are collected. We consider shear-thickening and shear-thinning fluids, under conditions of both common strain rate and common stress in the two phases, and present the four fundamental shear stress vs. strain rate curves and discuss their concentration dependence. We outline how to construct more complicated phase diagrams, discuss in which class various experimental systems fall, and sketch how to reconstruct the phase diagrams from rheological measurements

Local size segregation in polydisperse hard sphere fluids

The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and connect this, by a perturbation theory for narrow distributions, with the reversible work for changing the size of one particle in a monodisperse reference fluid.Comment: RevTeX, 4 pages, 3 figures, submitted to Phys. Rev. Let

Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.Comment: 32 pages, 6 figure