Experimental studies on taylor-couette flow of neutrally-buoyant suspensions

Abstract

The well known Taylor-Couette flow, the flow between two rotating concentric cylinders is used for studies on hydrodynamic stability, flow transitions and pattern formation (Andereck et al., 1986; Benjamin, 1978a,b; Coles, 1965; Fardin et al., 2014; Grossmann et al., 2016; Taylor, 1923, 1936a,b). The concentric cylinder geometry was initially used by Henry Mallock and Maurice Couette to measure viscosity of water (Couette, 1890; Mallock, 1889) and both came up with this idea independently. Mallock (1889) rotated inner cylinder keeping the outer cylinder fixed; he also did experiments with fixed inner cylinder and rotating outer cylinder. He found that at high velocities simple laminar flow was replaced by a complicated eddying flow. Couette (1890) kept the inner cylinder fixed and only rotated the outer cylinder. He measured the viscosity of water and found that it was constant up to a critical rotation rate. Rayleigh (1917) derived the inviscid instability criterion for cylindrical Couette flow between infinitely long concentric cylinders. He found that the flow is linearly stable if only the outer cylinder rotates, i.e. inner cylinder is at rest. Another form of the criteria is that the potential flow is unstable if the square of the circulation decreases outwards. This implies that the flow is centrifugally unstable for any inner cylinder rotation rate with a stationary outer cylinder.