Flow instability and transitions in Taylor–Couette flow of a semidilute non-colloidal suspension

Abstract

Abstract Flow of a semidilute neutrally buoyant and non-colloidal suspension is numerically studied in the Taylor–Couette geometry where the inner cylinder is rotating and the outer one is stationary. We consider a suspension with bulk particle volume fraction ${\\phi _b} = 0.1$, the radius ratio $(\\eta = {r_i}/{r_o} = 0.877)$ and two particle size ratios $\\mathrm{\\epsilon }\\,( = \\; d\\textrm{/}a) = 60,\\;200$, where d is the gap width ($= {r_o} - {r_i}$) between cylinders, a is the suspended particles’ radius and $r_i$ and $r_o$ are the inner and outer radii of the cylinder, respectively. Numerical simulations are conducted using the suspension balance model (SBM) and rheological constitutive laws. We predict the critical Reynolds number in which counter-rotating vortices arise in the annulus. It turns out that the primary instability appears through a supercritical bifurcation. For the suspension of $\\mathrm{\\epsilon } = 200$, the circular Couette flow (CCF) transitions via Taylor vortex flow (TVF) to wavy vortex flow (WVF). Additional flow states of non-axisymmetric vortices, namely spiral vortex flow (SVF) and wavy spiral vortex flow (WSVF) are observed between CCF and WVF for the suspension of $\\mathrm{\\epsilon } = 60$; thus, the transitions occur following the sequence of CCF → SVF → WSVF → WVF. Furthermore, we estimate the friction and torque coefficients of the suspension. Suspended particles substantially enhance the torque on the inner cylinder, and the axial travelling wave of spiral vortices reduces the friction and torque coefficients. However, the coefficients are practically the same in the WVF regime where particles are almost uniformly distributed in the annulus by the axial oscillating flow.