DERIVATION OF WENZEL’S AND CASSIE’S EQUATIONS FROM A PHASE FIELD MODEL FOR TWO PHASE FLOW ON ROUGH SURFACE∗
DERIVATION OF WENZEL’S AND CASSIE’S EQUATIONS FROM A PHASE FIELD MODEL FOR TWO PHASE FLOW ON ROUGH SURFACE∗
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发表时间：
2010
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通讯作者：
Xu Xianmin;Xiaoping Wang;X.-P. Wang
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文献类型：
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作者：
Xu Xianmin;Xiaoping Wang;X.-P. Wang
本文从最小化系统总自由能导出的相场方程出发，研究了粗糙表面上不互溶两相流体的平衡行为。当粗糙度变小时，我们利用多尺度展开均匀化技术导出了方程的有效边界条件。文泽尔方程和卡西方程的粗糙表面上的表观接触角，然后推导出有效的边界条件。用Γ-收敛理论严格证明了均匀化结果。
In this paper, the equilibrium behavior of an immiscible two phase fluid on a rough surface is studied from a phase field equation derived from minimizing the total free energy of the system. When the size of the roughness become small, we derive the effective boundary condition for the equation by the multiple scale expansion homogenization technique. The Wenzel’s and Cassie’s equations for the apparent contact angles on the rough surfaces are then derived from the effective boundary condition. The homogenization results are proved rigorously by the Γ-convergence theory.