Lubrication pressure model in a non-negligible gap for fluid permeation through a membrane with finite permeability
Lubrication pressure model in a non-negligible gap for fluid permeation through a membrane with finite permeability
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流体通过有限渗透率膜的不可忽略间隙中的润滑压力模型
DOI：
10.1103/physrevfluids.6.114101
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发表时间：
2021
影响因子：
2.7
通讯作者：
Kajishima Takeo
中科院分区：
文献类型：
--
作者：
Takeuchi Shintaro;Fukada Toshiaki;Yamada Shuji;Miyauchi Suguru;Kajishima Takeo
发生在壁附近的流体的膜渗透受到润滑的强烈影响，因为所产生的压力加速流体通过膜。在本研究中，由润滑压力驱动的纯流体的膜渗透建模为一般壁膜几何形状，以了解渗透率对渗透通量的影响，在一个范围内的壁膜间隙宽度，不能处理的雷诺润滑方程。这种润滑效应（称为非雷诺润滑效应）建模包括一个高阶压力分量所描述的壁切向导数的本地Couette-Poietille速度，和渗透通量模型与非雷诺润滑效应的开发。渗透模型用放置在具有固定纵横比（即，平均壁-膜距离与纵向膜长度之比）为0.1。通过改变无因次渗透率，研究了膜与壁面之间润滑压力驱动的渗透。在一个无穷小的渗透率，渗透通量模型显示出良好的协议与充分解决的数值模拟，由于可比的贡献Couette和Poiffille组件的渗透模型，而渗透模型表现出发散的趋势，在有限的渗透率，因为Couette组件在模型中产生了过度的贡献，润滑压力。然而，通过将简化的重整化过程应用于Couette分量到最低阶压力分量，发散趋势被抑制，并且再现了有限渗透率范围内的渗透通量。根据壁膜间隙和渗透率范围的条件，讨论了重整化基团渗透模型的适用性。
The membrane permeation of a fluid occurring near the wall is strongly influenced by lubrication because the generated pressure accelerates the fluid passing through the membrane. In the present study, the membrane permeation of a pure fluid driven by the lubrication pressure is modeled for a general wall-membrane geometry to understand the effect of permeability on the permeate flux in a range of wall-membrane gap widths that cannot be treated by the Reynolds lubrication equation. This lubrication effect (referred to as the non-Reynolds lubrication effect) is modeled by including a higher-order pressure component described by the wall-tangential derivative of the local Couette-Poiseuille velocity, and a permeate flux model with the non-Reynolds lubrication effect is developed. The permeation model is validated with a corrugated membrane placed in a two-dimensional parallel channel with a fixed aspect ratio (i.e., the average wall-membrane distance to the longitudinal membrane length) of 0.1. The permeation driven by the lubrication pressure between the membrane and wall is studied by varying the nondimensional permeability. At an infinitesimal permeability, the permeate flux model shows good agreement with the fully resolved numerical simulation owing to the comparable contribution of the Couette and Poiseuille components in the permeation model, whereas the permeation model exhibits a diverging trend at finite permeabilities because the Couette component in the model produces an excessive contribution to the lubrication pressure. However, by applying a simplified renormalization procedure to the Couette component into the lowest-order pressure component, the diverging trend is suppressed and the permeate flux in a finite permeability range is reproduced. The applicability of the renormalization-group permeation model is discussed in terms of the conditions of the wall-membrane gap and permeability range.