Abstract
We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius a. By analyzing the inertial lift force, we argue that this force is proportional to a3b, where b is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on b and is equal to that of the sphere of radius a.
Highlights
It is well-known that at finite Reynolds numbers, particles migrate across streamlines of the flow to some equilibrium positions in the microchannel
We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by a pressure gradient
By analyzing the inertial lift force, we argue that this force is proportional to a3b, where b is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on b and is equal to that of the sphere of radius a
Summary
It is well-known that at finite Reynolds numbers, particles migrate across streamlines of the flow to some equilibrium positions in the microchannel. Roth et al. recently reported the separation of spheres, ellipsoids, and peanut-shaped particles in a spiral microfluidic device, where the inertial lift force is balanced by the Dean force that can be generated in curved channels.13 These papers concluded that a key parameter defining equilibrium positions of particles is their rotational diameter. We present some results of an LBM study of the inertial migration of oblate spheroids in a plane channel, where the steady laminar flow of moderate Re is generated by a pressure gradient. To predict their long-term migration, we have to find a lift force for this steady configuration Once it is known, the equilibrium positions of oblate spheroids (including non-neutrally buoyant too) can be found by balancing the lift and external forces
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