论文标题
用一种非牛顿流体的两流体泰勒 - 库特流量分析
Analysis of a two-fluid Taylor-Couette flow with one non-Newtonian fluid
论文作者
论文摘要
我们研究了两个粘性缸之间的两种粘性流体膜的动态行为，它们以较小的相对速度旋转。假定流体是不混溶的，并且与内部流体的体积相比，外流体膜的体积很大。此外，虽然外部流体被认为具有恒定的粘度，但内部薄膜的流变行为由应变依赖性幂律确定。从Navier-Stokes系统开始，我们正式得出了分隔两种流体的界面的演化方程。两种竞争效应驱动界面的动力学，即表面张力和圆柱旋转引起的剪切应力。当两种效果是可比的时，解决方案在很大程度上表现得像牛顿政权一样。我们还研究了表面张力效应主导圆柱体旋转引起的应力的状态。在这种情况下，我们证明了用于剪切稀释和剪切厚的液体的局部较弱溶液的存在。在后一种情况下，我们表明，最初接近圆的接口在有限的时间内收敛到圆圈，并保留以后的时间。
We study the dynamic behaviour of two viscous fluid films confined between two concentric cylinders rotating at a small relative velocity. It is assumed that the fluids are immiscible and that the volume of the outer fluid film is large compared to the volume of the inner one. Moreover, while the outer fluid is considered to have constant viscosity, the rheological behaviour of the inner thin film is determined by a strain-dependent power-law. Starting from a Navier--Stokes system, we formally derive evolution equations for the interface separating the two fluids. Two competing effects drive the dynamics of the interface, namely, the surface tension and the shear stresses induced by the rotation of the cylinders. When the two effects are comparable, the solutions behave, for large times, as in the Newtonian regime. We also study the regime in which the surface tension effects dominate the stresses induced by the rotation of the cylinders. In this case, we prove local existence of positive weak solutions both for shear-thinning and shear-thickening fluids. In the latter case, we show that interfaces which are initially close to a circle converge to a circle in finite time and keep that shape for later times.
