剪切分层系统中的桥长和时标：从Cahn-Hilliard到Doi-Ohta模型
Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model
摘要：
我们开发了一个系统的粗粒化程序，建立在不同的长度和时间尺度的不混溶流体的混合物模型之间的连接。我们从Cahn-Hilliard模型的亚稳分解在一个二元流体混合物下流动，我们从中获得粗粒度的描述。这个过程中的关键步骤是识别相关的粗粒度变量，并找到适当的映射，以更微观的变量来表达它们。为了捕捉的Doi-Ohta水平的物理，我们引入的界面宽度作为一个额外的变量在该水平。通过这种方式，我们考虑了流动下的界面拉伸，并解析地推导出相关粗粒度变量的对流行为，在长波长极限下恢复了熟悉的现象学Doi-Ohta模型。此外，我们得到的Cahn-Hilliard参数作为一个直接的结果开发的粗粒化过程中的界面张力的表达式。最后，通过对Cahn-Hilliard模型的数值模拟结果的分析，讨论了Doi-Ohta模型中的耗散过程与Cahn-Hilliard模型中的耗散过程是同源的。建立了从Cahn-Hilliard水平模拟的底层形态动力学来估计Doi-Ohta模型的界面弛豫时间的方法。
英文摘要：
We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
