Inertial migration of a rigid sphere in plane Poiseuille flow as a test of dissipative particle dynamics simulations

After reviewing and organizing the literature on the problem of inertial cross-stream migration of rigid spheres in various geometries including tubes and channels, we use Dissipative Particle Dynamics (DPD) simulations to study the simplest case of migration of a single neutrally or non-neutrally buoyant sphere with diameter 20% of the gap in plane Poiseuille flow and assess the potential and limitations of DPD simulations for this and similar problems. We find that the neutrally buoyant sphere lags by up to 6% behind the surrounding fluid and is focused at a position around 50% of the distance between the channel center and the wall. With Re increasing from around 100 to 500, the sphere migrates closer to the channel center. With flow driven by gravity, a much denser non-neutrally buoyant sphere leads the surrounding fluid and is focused at a position closer to the wall, around 60% the distance from the channel center to the wall, in qualitative agreement with previous work. The lower values of the Schmidt number Sc in DPD simulations relative to real fluids, due to the relatively large diffusivity of DPD beads, are shown to not significantly affect the consistency of our DPD results with literature results although they make results noisy at low Re (i.e., $$ 50). However, the increase in Ma and Wi with increasing Re leads to compressible flow effects and in some cases viscoelastic effects at high Re depending on the DPD parameters chosen. Even for optimally chosen parameters, we require $$ to avoid strong compressibility effects. Thus, the relative simplicity of the DPD method for complex fluid flows is offset by the need to control the effects of unphysically high values of other parameters, such as Ma and Wi, which seriously limits the range of conditions under which DPD simulations give valid results in fluid transport problems.