Neelamegam R, Giribabu D, Shankar V
Department of Chemical Engineering, Indian Institute of Technology, Kanpur 208016, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):043004. doi: 10.1103/PhysRevE.90.043004. Epub 2014 Oct 7.
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.
通过实验探究了粘性流体流过柔软双层凝胶时流动的不稳定性，并将观测结果与线性稳定性分析的结果进行了比较。实验系统由流变仪的旋转顶板及其放置双层凝胶的固定底板组成。当顶板与双层凝胶之间的流动为测粘流动（即层流）时，流变仪测得的粘度是流体材料特性的一种度量。然而，在临界剪切应力之后，表观粘度会突然增加，这表明由于双层凝胶的可变形性质，流动发生了不稳定性。进行实验以量化使流动失稳所需的流体剪切应力临界值如何随固体与流体层厚度之比以及两种凝胶的剪切模量之比而变化。通过假设两个固体层为弹性新胡克材料，对牛顿流体流过双层凝胶的平面库埃特流进行了线性稳定性分析。为了比较实验和理论结果，发现双层凝胶的有效剪切模量（由(H/Geff = H1/G1 + H2/G2)定义）很有用，其中(H = H1 + H2)。这里，(Hi)和(Gi)（(i = 1, 2)）分别表示每层的厚度和剪切模量。从稳定性分析得到的无量纲参数(\Gamma eff = ηV/(dGeff))（(V)是顶板速度；(η)是流体粘度，(d)是流体厚度）作为固体与流体厚度(H/d)的函数的结果与实验观测结果吻合良好，无需任何拟合参数。一般来说，我们发现与较硬凝胶与流体流动相邻的情况相比，较软凝胶与流体流动相邻时流动更不稳定。这表明这种不稳定性本质上更具界面性，并且关键取决于两层的相对位置，而不仅仅取决于双层凝胶的有效模量。我们进一步表明，双层凝胶的理论和实验数据可以适当地归纳为单层凝胶的结果。
