Taylor-Couette instability in sphere suspensions

We employ a rheological theory to show that circular Taylor-Couette flow of a suspension of non-Brownian spheres is less stable than that of a Newtonian fluid, at equal effective viscosity. The destabilization is related to the preferred orientation of the separation vector of the closely interacting spheres, in the compressive direction of the base flow. The results agree qualitatively with experimental observations from the literature.

Figure 1

The critical, effective Taylor number $\mathrm{Ta}$ [Eq. (1)] as a function of the sphere volume fraction $\varphi$. Comparison between the experimental data of Ref. [4] (markers), the two-fluid theory of Ref. [5] (solid line), and the present rheological theory (dashed line).

Figure 2

The sphere pair separation unit vector $\mathit{n}$.

Figure 3

The computed, critical, effective Taylor number $\mathrm{Ta}$ [Eq. (1)] as a function of the normalized, spanwise wave number $k\mathrm{\Delta }R/\pi$, for the Newtonian fluid (sphere volume fraction $\varphi =0$; solid line) and for a suspension with $\varphi =0.5$ (dashed line). The vertical, dotted line coincides with the minima of the curves.

Figure 4

(top) Most unstable eigenmode in the Newtonian fluid, i.e., using a sphere volume fraction of $\varphi =0$, and a Taylor number [Eq. (1)] at the critical value of $\mathrm{Ta}\approx 44$. (bottom) Most unstable axisymmetric eigenmode in a sphere suspension, using a sphere volume fraction of $\varphi =0.5$, and an effective Taylor number [Eq. (1)] at the critical value of $\mathrm{Ta}\approx 28$.