Lattice Boltzmann simulations of a viscoelastic shear-thinning fluid

We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear integral constitutive equation, relating the stress tensor locally to the history of flow. As an application, we present results for an integral nonlinear Maxwell model that combines the effects of (linear) viscoelasticity and (nonlinear) shear thinning. We discuss the transient dynamics of velocities, shear stresses, and normal stress differences in planar pressure-driven channel flow, after switching on (startup) and off (cessation) of the driving pressure. This transient dynamics depends nontrivially on the channel width due to an interplay between hydrodynamic momentum diffusion and slow structural relaxation

A Simplest Swimmer at Low Reynolds Number: Three Linked Spheres

We propose a very simple one-dimensional swimmer consisting of three spheres that are linked by rigid rods whose lengths can change between two values. With a periodic motion in a non-reciprocal fashion, which breaks the time-reversal symmetry as well as the translational symmetry, we show that the model device can swim at low Reynolds number. This model system could be used in constructing molecular-size machines

Drag Reduction by Bubble Oscillations

Drag reduction in stationary turbulent flows by bubbles is sensitive to the dynamics of bubble oscillations. Without this dynamical effect the bubbles only renormalize the fluid density and viscosity, an effect that by itself can only lead to a small percentage of drag reduction. We show in this paper that the dynamics of bubbles and their effect on the compressibility of the mixture can lead to a much higher drag reduction.Comment: 7 pages, 1 figure, submitted to Phys. Rev.

Channel Flow of a Tensorial Shear-Thinning Maxwell Model: Lattice Boltzmann Simulations

We introduce a nonlinear generalized tensorial Maxwell-type constitutive equation to describe shear-thinning glass-forming fluids, motivated by a recent microscopic approach to the nonlinear rheology of colloidal suspensions. The model captures a nonvanishing dynamical yield stress at the glass transition and incorporates normal-stress differences. A modified lattice-Boltzmann (LB) simulation scheme is presented that includes non-Newtonian contributions to the stress tensor and deals with flow-induced pressure differences. We test this scheme in pressure-driven 2D Poiseuille flow of the nonlinear generalized Maxwell fluid. In the steady state, comparison with an analytical solution shows good agreement. The transient dynamics after startup and cessation of the pressure gradient are studied; the simulation reproduces a finite stopping time for the cessation flow of the yield-stress fluid in agreement with previous analytical estimates

Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms

A simple set of algebraic equations is derived for the exact low-temperature thermodynamics of one-dimensional multi-component strongly attractive fermionic atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For linear Zeeman splitting, the physics of the gapless phase at low temperatures belongs to the universality class of a two-component asymmetric TLL corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms. The equation of states is also obtained to open up the study of multi-component TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

Hydrodynamic phase-locking of swimming microorganisms

Some microorganisms, such as spermatozoa, synchronize their flagella when swimming in close proximity. Using a simplified model (two infinite, parallel, two-dimensional waving sheets), we show that phase-locking arises from hydrodynamics forces alone, and has its origin in the front-back asymmetry of the geometry of their flagellar waveform. The time-evolution of the phase difference between co-swimming cells depends only on the nature of this geometrical asymmetry, and microorganisms can phase-lock into conformations which minimize or maximize energy dissipation

Evidence for the super Tonks-Girardeau gas

We provide evidence in support of a recent proposal by Astrakharchik at al. for the existence of a super Tonks-Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the super T-G gas-like stat

Motion and homogenization of vortices in anisotropic Type II superconductors

The motion of vortices in an anisotropic superconductor is considered. For a system of well-separated vortices, each vortex is found to obey a law of motion analogous to the local induction approximation, in which velocity of the vortex depends upon the local curvature and orientation. A system of closely packed vortices is then considered, and a mean field model is formulated in which the individual vortex lines are replaced by a vortex density

Shear flow pumping in open microfluidic systems

We propose to drive open microfluidic systems by shear in a covering fluid layer, e.g., oil covering water-filled chemical channels. The advantages as compared to other means of pumping are simpler forcing and prevention of evaporation of volatile components. We calculate the expected throughput for straight channels and show that devices can be built with off-the-shelf technology. Molecular dynamics simulations suggest that this concept is scalable down to the nanoscale.Comment: 4 pages, 4 figure, submitted to Phys. Rev. Let