二维和三维剪切驱动相分离的流动参数调控
Flow-parametric regulation of shear-driven phase separation in two and three dimensions
摘要：
研究了二维和三维Cahn-Hilliard方程的混沌剪切流。主要目标是比较和对比的相分离在二维和三维，使用高分辨率的数值模拟作为研究的基础。模型流的振幅（从而承认各向异性的可能性），lengthscales，和多个时间尺度的参数化，和相分离的结果作为这些参数的函数，以及维数的调查。以这种方式，一个参数政权被确定，其中相分离和相关的粗化现象不仅被逮捕，但事实上的浓度方差衰减，从而打开了描述的浓度场的动态使用的平流扩散理论的可能性。该参数区域对应于长流量相关时间、大流量振幅和小扩散系数。这种高扩散制度的发病解释引入巴彻勒长度尺度。一个关键的结果是，在hyperdiffusive制度，浓度的分布（特别是浓度的极值的频率）强烈依赖于维数。各向异性的情况下也进行了研究：对于其中的方差饱和（对应于粗化逮捕）的情况下，域对齐的方向取决于流相关时间。因此，对于与平均剪切速率的倒数相当的相关时间，域在最大流动振幅的方向上对齐，而对于短的相关时间，域最初在相反的方向上对齐。然而，在非常晚的时间（在经过数千个相关时间之后），域的命运是相同的，与相关时间无关，即在最大流动幅度的方向上对齐。
英文摘要：
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical simulation as the basis for the study. The model flow is parametrized by its amplitudes (thereby admitting the possibility of anisotropy), lengthscales, and multiple time scales, and the outcome of the phase separation is investigated as a function of these parameters as well as the dimensionality. In this way, a parameter regime is identified wherein the phase separation and the associated coarsening phenomenon are not only arrested but in fact the concentration variance decays, thereby opening up the possibility of describing the dynamics of the concentration field using the theories of advection diffusion. This parameter regime corresponds to long flow correlation times, large flow amplitudes and small diffusivities. The onset of this hyperdiffusive regime is interpreted by introducing Batchelor lengthscales. A key result is that in the hyperdiffusive regime, the distribution of concentration (in particular, the frequency of extreme values of concentration) depends strongly on the dimensionality. Anisotropic scenarios are also investigated: for scenarios wherein the variance saturates (corresponding to coarsening arrest), the direction in which the domains align depends on the flow correlation time. Thus, for correlation times comparable to the inverse of the mean shear rate, the domains align in the direction of maximum flow amplitude, while for short correlation times, the domains initially align in the opposite direction. However, at very late times (after the passage of thousands of correlation times), the fate of the domains is the same regardless of correlation time, namely alignment in the direction of maximum flow amplitude.
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