A novel model for the lift force acting on a prolate spheroidal particle in an arbitrary non-uniform flow. Part I. Lift force due to the streamwise flow shear

The paper proposes a generic method to extend lift force models that were originally devised for single linear shear flow, to arbitrary flow conditions. The method computes the lift force due to the dominant streamwise flow shear in the Stokes flow regime by implementing a series of coordinate transformations, facilitating the computation of the lift force from dominant streamwise flow shear. The derived numerical algorithm is applied to the computation of a dedicated shear lift force model for prolate spheroidal particles (or axisymmetric ellipsoidal particles) and a novel generalised Saffman-type lift force model for spherical particles in a general shear flow. In order to verify the proposed shear lift force for prolate spheroidal particles, numerical simulations of a particle moving in Poiseuille flow at four different initial positions and two aspect ratios are perfomed. The new generalised Saffman-type lift model is compared with an established generalised Saffman-type lift model by simulating the axial migration of a spherical particle in Poiseuille flow. The computational results confirm the correctness of the proposed shear lift force models.