A variational approach to moving contact line hydrodynamics
A variational approach to moving contact line hydrodynamics
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DOI：
10.1017/s0022112006001935
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发表时间：
2006-02
影响因子：
3.7
通讯作者：
T. Qian;Xiaoping Wang;P. Sheng
中科院分区：
文献类型：
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作者：
T. Qian;Xiaoping Wang;P. Sheng
在不相容的两相流中，接触线表示流体-流体界面与固体壁的交点。当一种流体取代另一种流体时，接触线就会沿壁面移动。连续介质流体力学中的一个经典问题是运动接触线与无滑移边界条件之间的不相容，因为无滑移边界条件导致了不可积奇异性。最近发现的广义Navier边界条件(GNBC)提供了一种替代无滑移边界条件的方法，可以解决移动接触线难题。我们通过最小能量耗散(熵产生)原理给出了GNBC的变分推导，这是Onsager对于远离平衡的小扰动所提出的。通过对一个连续介质流体动力学模型的数值实现，证明了GNBC可以定量地再现分子动力学模拟得到的运动接触线滑移速度分布。特别地，从运动接触线处的完全滑移到远处的近零滑移的转变被证明是由一个扩展到介观长度尺度的幂定律部分滑移区域所控制的。讨论了流体动力学模型的流体-流体界面极限，以及滑移与不滑移的一些一般含义。
In immiscible two-phase flows, the contact line denotes the intersection of the fluid–fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation of the GNBC through the principle of minimum energy dissipation (entropy production), as formulated by Onsager for small perturbations away from equilibrium. Through numerical implementation of a continuum hydrodynamic model, it is demonstrated that the GNBC can quantitatively reproduce the moving contact line slip velocity profiles obtained from molecular dynamics simulations. In particular, the transition from complete slip at the moving contact line to near-zero slip far away is shown to be governed by a power-law partial-slip regime, extending to mesoscopic length scales. The sharp (fluid–fluid) interface limit of the hydrodynamic model, together with some general implications of slip versus no slip, are discussed.