Instability of viscous flow over a deformable two-layered gel: experiments and theory.

The instability of the flow of a viscous fluid past a soft, two-layered gel is probed using experiments, and the observations are compared with results from a linear stability analysis. The experimental system consists of the rotating top plate of a rheometer and its stationary bottom plate on which the two-layer gel is placed. When the flow between the top plate and the two-layer gel is viscometric (i.e., laminar), the viscosity obtained from the rheometer is a measure of the material property of the fluid. However, after a critical shear stress, there is a sudden increase in apparent viscosity, indicating that the flow has undergone an instability due to the deformable nature of the two-layer gel. Experiments are carried out to quantify how the critical value of fluid shear stress required to destabilize the flow varies as a function of ratio of solid to fluid layer thickness, and the ratio of the shear moduli of the two gels. A linear stability analysis is carried out for plane Couette flow of a Newtonian fluid past the two-layered gel, by assuming the two solid layers to be elastic neo-Hookean materials. In order to compare the experimental and theoretical results, the effective shear modulus (Geff, defined by H/Geff=H1/G1+H2/G2) of the two-layer gel is found to be useful, where H=H1+H2. Here, Hi and Gi (i=1,2), respectively, denote the thickness and shear modulus of each layer. Results for the nondimensional parameter Γeff=ηV/(dGeff) (V is the velocity of the top plate; η is fluid viscosity, d is the fluid thickness) as a function of solid to fluid thickness H/d obtained from the stability analysis agree well with experimental observations, without any fitting parameters. In general, we find that the flow is more unstable if the softer gel is adjacent to the fluid flow compared to the case when it is not. This suggests that the instability is more interfacial in nature and is crucially dependent on the relative placement of the two layers, and not just on the effective modulus of the two-layer gel. We further show that the theoretical and experimental data for two-layer gels can be suitably collapsed onto the results obtained for a single-gel layer.