Negative Saffman-like Lift in Granular Shear Flows

We consider the lift and drag forces on a spherical intruder particle in a uniform shear flow of smaller spherical particles in the absence of gravity as a function of the imposed streamwise slip velocity. Surprisingly, the net force perpendicular to the shear plane, or lift force, on the intruder due to contacts with bed particles is in the opposite direction of the classical Saffman lift in sheared fluids. To better understand this difference, we compare discrete element method (DEM) simulations of an intruder in a sheared granular flow to corresponding finite volume simulations for an intruder in a sheared Newtonian fluid over a wide range of slip velocities. In a sheared granular bed the granular medium cannot sustain tension and, consequently, a void forms on the downstream side of the intruder at high enough slip velocities. To mimic this void effect in the fluid simulation results, we integrate the fluid stress only on a restricted region of the intruder, which flips the intruder lift force in the fluid to match the lift force direction in the granular material. Truncating the fluid stress in this fashion also produces lift and drag force magnitudes comparable to those in the granular system. This material is based upon work supported by the National Science Foundation under Grant No. CBET-1929265.