We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required.PACS numbers: 47.63. Gd, 87.10.Mn, 87.17.Jj The motility of microorganisms raises basic physics questions that range from local swimming mechanisms [1-3] to many-body emergent phenomena [4,5,7]. In the latter context, even grossly simplified models represent a challenging and active area of nonequilibrium statistical mechanics [4]. In some cases experimental nearcounterparts to these models can be devised in which various complicating factors (cell division, chemotaxis, etc.) are environmentally or genetically suppressed [8].Indeed certain bacteria, including E. coli, exhibit motion which can be idealized as a 'run-and-tumble' model. Here straight 'runs' at constant speed v are punctuated by sudden, rapid and complete randomizations in direction, or 'tumbles', occurring stochastically with rate α [8]. The mean run length is = v/α and duration 1/α; at larger length and time scales Fick's law is obeyed, with diffusivity D = v 2 /dα in d dimensions [9]. This model offers an important paradigm for a diffusion process that is fundamentally non-Brownian. Subtle consequences of this are manifest for particles in external force fields, such as gravity or a harmonic trap [10]. In the first case, the gravitational decay length λ falls strictly to zero when the gravitational force f exceeds the propulsive force f p , in contrast to Brownian particles for which λ = D/f [10]. In a harmonic trap (f = −kr), particles are strictly confined within a radius r * = f p /k; and for > ∼ r * the maximum density occurs at r ∼ r * not r = 0. In this limit, a particle in the trap interior rapidly swims out to r * and stays there a long time until its next tumble [10].The qualitative physics of the aforementioned results is robust to both a distribution in v, or a residual true Brownian diffusivity. On the other hand, because there is no underlying free energy (which would give a Boltzmann distribution as the unique steady state), long-range hydrodynamic interactions (HI) between the particles could have major consequences, even for steady-state behavior. Several computational approaches to address hydrodynamics have been developed [5], but none have addressed the basic physics problems considered below: (a) sedimentation in a container with a solid bottom; (b) confinement by a harmonic trap; and (c) Poiseuille flow between parallel plates. These we consider at small but finite particle density, so that in (a,b) only the far-field hydrodynamics are important. In (c),...

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There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In this paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

We present an accurate method to include arbitrary singular distributions of forces in the lattice Boltzmann formulation of hydrodynamics. We validate our method with several examples involving Stokeslet, stresslet, and rotlet singularities, finding excellent agreement with analytical results. A minimal model for sedimenting particles is presented using the method. In the dilute limit, this model has accuracy comparable to, but computational efficiency much greater than, algorithms that explicitly resolve the size of the particles.