Inertial migration of neutrally buoyant particles in a square duct has been investigated by numerical simulation in the range of Reynolds numbers from 100 to 1000. Particles migrate to one of a small number of equilibrium positions in the cross-sectional plane, located near a corner or at the center of an edge. In dilute suspensions, trains of particles are formed along the axis of the flow, near the planar equilibrium positions of single particles. At high Reynolds numbers ͑Reജ 750͒, we observe particles in an inner region near the center of the duct. We present numerical evidence that closely spaced pairs of particles can migrate to the center at high Reynolds number.In Poiseuille flow, a neutrally buoyant particle migrates to a position that is determined by the balance of forces generated by the gradient of the shear rate and interactions of the flow field with the container walls. In a cylindrical flow, uniformly distributed particles migrate to form a stable ring located at approximately 0.6R, where R is the radius of the cylinder. 1 Theoretical calculations for small particles in planar Poiseuille flow give equilibrium positions similar to those observed experimentally. 2,3 Asmolov 3 extended the method of matched asymptotic expansions 2 to a higher Reynolds number, obtaining good agreement with experiment 4 up to Re= UD / = 1700, where turbulent flow was first observed. Here, U is the average flow velocity, D is the cylinder diameter, and is the kinematic viscosity of the fluid. The profile of the lateral force across the channel shows only one equilibrium position, which shifts closer to the boundary wall as the Reynolds number increases. Our interest in this problem was sparked by two recent experimental observations: first that particles tend to align near the walls to make linear chains of more or less equally spaced particles, 1,5 and second that at high Reynolds numbers ͑Reϳ 1000͒, an additional inner ring of particles was observed when the ratio of particle diameter d to cylinder diameter was of the order of 1:10. 4 Large particles introduce an additional Reynolds number, Re p =Re͑d / D͒ 2 , which may not be small, as assumed theoretically. 2,3 In this work, inertial migration of neutrally buoyant particles has been investigated by numerical simulation in the range of Reynolds numbers from 100 to 1000. We have focused on large particles, with a diameter of about 1 / 10 of the channel dimension ͑H͒. Initially we studied a pressuredriven channel flow, but we found only a single equilibrium position, in close agreement with theory. To investigate the effects of geometry we next studied a square duct, which was simpler for our code than a cylinder. Here we found that an isolated sphere migrates to one of a discrete set of equilibrium positions, depending on initial conditions. We discuss the evolution of these equilibrium positions with the Reynolds number. In dilute suspensions, we observed linear chains of particles being formed in the flow direction, similar to what has been seen in laboratory exper...

Several different interpolation schemes have been proposed for improving the accuracy of lattice Boltzmann simulations in the vicinity of a solid boundary. However, these methods require at least two or three fluid nodes between nearby solid surfaces, a condition that may not be fulfilled in dense suspensions or porous media for example. Here we propose an interpolation of the equilibrium distribution, which leads to a velocity field that is both second-order accurate in space and independent of viscosity. The equilibrium interpolation rule infers population densities on the boundary itself to reduce the span of nodes needed for interpolation; it requires a minimum of one grid spacing between the nodes. By contrast, the linear interpolation rule requires two fluid nodes in the gap and leads to a viscosity-dependent slip velocity, while the multireflection rule is viscosity independent but requires a minimum of three fluid nodes.

The sharkskin-mimetic, patterned TFC RO membranes exhibited superior biofouling resistance compared to conventional and simple patterned membranes.