Critical elastic number for the elasto-inertial migration of spheroid in confined microchannel of viscoelastic fluids

Abstract

The critical elastic number for the elasto-inertial migration of spheroid in confined microchannel of viscoelastic fluid is numerically studied by the direct forcing/fictitious domain (DF/FD) method. The effect of the blockage ratio (k), aspect ratio (α), initial orientation and position of the particles, and the fluid elastic number (El) on the changes of equilibrium position and rotational behavior are explored, respectively. The results show that the confined microchannel reduce the number of rotational modes, prolate (oblate) spheroid exhibit four (three) kinds of rotational modes. The channel centreline (CC), diagonal line (DL) and cross-section midline (CSM) equilibrium positions are found within the present simulated parameters. For the first time, the prolate and oblate spheroid keeping the stable CC and DL equilibrium positions are simultaneously observed, but this phenomenon does not exist for spherical particles or small-sized spheroids. The strength of the particle induced-convection is a strong function of particle size, large particles are more susceptible to fluid inertia and migrate diagonally to the DL equilibrium position. Approaching the critical elastic number, particles can sudden change from the DL equilibrium position to the CC equilibrium position, the rotational modes are complex and depend on the fluid elastic number, the particle shape and size. The larger particles have the higher critical elastic number for equilibrium position transition than the small particles. Prolate spheroids have the smallest critical elastic number, then followed by sphere, the oblate spheroids require the highest elastic number to the CC equilibrium position.