Collision of microswimmers in a viscous fluid

Asymptotics and Summation of the Effective Properties of Suspensions, Simple Liquids and Composites

We review the problem of summation for a very short truncation of a power series by means of special resummation techniques inspired by the field-theoretical renormalization group. Effective viscosity (EV) of active and passive suspensions is studied by means of a special algebraic renormalization approach applied to the first and second-order expansions in volume fractions of particles. EV of the 2D and 3D passive suspensions is analysed by means of various self-similar approximants such as iterated roots, exponential approximants, super-exponential approximants and root approximants. General formulae for all concentrations are derived. A brief introduction to the rheology of micro-swimmers is given. Microscopic expressions for the intrinsic viscosity of the active system of puller-like microswimmers are obtained. Special attention is given to the problem of the calculation of the critical indices and amplitudes of the EV and to the sedimentation rate in the vicinity of known critical points. Critical indices are calculated from the short truncation by means of minimal difference and minimal derivative conditions on the fixed points imposed directly on the critical properties. Accurate expressions are presented for the non-local diffusion coefficient of a simple liquid in the vicinity of a critical point. Extensions and corrections to the celebrated Kawasaki formula are discussed. We also discuss the effective conductivity for the classical analog of graphene and calculate the effective critical index for superconductivity dependent on the concentration of vacancies. Finally, we discuss the effective conductivity of a random 3D composite and calculate the superconductivity critical index of a random 3D composite.

Bacterial biomechanics-From individual behaviors to biofilm and the gut flora

Bacteria inhabit a variety of locations and play important roles in the environment and health. Our understanding of bacterial biomechanics has improved markedly in the last decade and has revealed that biomechanics play a significant role in microbial biology. The obtained knowledge has enabled investigation of complex phenomena, such as biofilm formation and the dynamics of the gut flora. A bottom-up strategy, i.e., from the cellular to the macroscale, facilitates understanding of macroscopic bacterial phenomena. In this Review, we first cover the biomechanics of individual bacteria in the bulk liquid and on surfaces as the base of complex phenomena. The collective behaviors of bacteria in simple environments are next introduced. We then introduce recent advances in biofilm biomechanics, in which adhesion force and the flow environment play crucial roles. We also review transport phenomena in the intestine and the dynamics of the gut flora, focusing on that in zebrafish. Finally, we provide an overview of the future prospects for the field.

Random sets of stadiums in square and collective behavior of bacteria

Collective motion of swimmers can be detected by hydrodynamic interactions through the eective (macroscopic) viscosity. It follows form the general hydrodynamics that the eective viscosity of non-dilute random suspensions depends on the shape of particles and of their spacial probabilistic distribution. Therefore, a comparative analysis of disordered and collectively interacting particles of the bacteria shape can be done in terms of the probabilistic geometric parameters which determine the eective viscosity. In this paper, we develop a quantitative criterion to detect the collective behavior of bacteria. This criterion is based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums) which characterize the high-order correlation functions. The locations and the shape of bacteria are modeled by stadiums randomly embedded in medium without overlapping. This shape models can be considered as improvement of the previous segment model.We calculate the e-sums of the simulated disordered sets and of the observed experimental locations of bacteria subtilis. The obtained results show a dierence between these two sets that demonstrates the collective motion of bacteria.

A criterion of collective behavior of bacteria

It was established in the previous works that hydrodynamic interactions between the swimmers can lead to collective motion. Its implicit evidences were confirmed by reduction in the effective viscosity. We propose a new quantitative criterion to detect such a collective behavior. Our criterion is based on a new computationally effective RVE (representative volume element) theory based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums). The criterion can be applied to various two-phase dispersed media (biological systems, composites etc). The locations of bacteria are modeled by short segments having a small width randomly embedded in medium without overlapping. We compute the e-sums of the simulated disordered sets and of the observed experimental locations of Bacillus subtilis. The obtained results show a difference between these two sets that demonstrates the collective motion of bacteria.

Shape matters: Near-field fluid mechanics dominate the collective motions of ellipsoidal squirmers

Microswimmers show a variety of collective motions. Despite extensive study, questions remain regarding the role of near-field fluid mechanics in collective motion. In this paper, we describe precisely the Stokes flow around hydrodynamically interacting ellipsoidal squirmers in a monolayer suspension. The results showed that various collective motions, such as ordering, aggregation, and whirls, are dominated by the swimming mode and the aspect ratio. The collective motions are mainly induced by near-field fluid mechanics, despite Stokes flow propagation over a long range. These results emphasize the importance of particle shape in collective motion.

Macroscopic equations for bacterial chemotaxis: integration of detailed biochemistry of cell signaling

Chemotaxis of single cells has been extensively studied and a great deal on intracellular signaling and cell movement is known. However, systematic methods to embed such information into continuum PDE models for cell population dynamics are still in their infancy. In this paper, we consider chemotaxis of run-and-tumble bacteria and derive continuum models that take into account of the detailed biochemistry of intracellular signaling. We analytically show that the macroscopic bacterial density can be approximated by the Patlak-Keller-Segel equation in response to signals that change slowly in space and time. We derive, for the first time, general formulas that represent the chemotactic sensitivity in terms of detailed descriptions of single-cell signaling dynamics in arbitrary space dimensions. These general formulas are useful in explaining relations of single cell behavior and population dynamics. As an example, we apply the theory to chemotaxis of bacterium Escherichia coli and show how the structure and kinetics of the intracellular signaling network determine the sensing properties of E. coli populations. Numerical comparison of the derived PDEs and the underlying cell-based models show quantitative agreements for signals that change slowly, and qualitative agreements for signals that change extremely fast. The general theory we develop here is readily applicable to chemotaxis of other run-and-tumble bacteria, or collective behavior of other individuals that move using a similar strategy.