Rey AD
Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 2B2.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1540-9. doi: 10.1103/physreve.61.1540.
A complete macroscopic theory for compressible nematic-viscous fluid interfaces is developed and used to characterize the interfacial elastic, viscous, and viscoelastic material properties. The derived expression for the interfacial stress tensor includes elastic and viscous components. Surface gradients of the interfacial elastic stress tensor generates tangential Marangoni forces as well as normal forces. The latter may be present even in planar surfaces, implying that in principle static planar interfaces may accommodate pressure jumps. The asymmetric interfacial viscous stress tensor takes into account the surface nematic ordering and is given in terms of the interfacial rate of deformation and interfacial Jaumann derivative. The material function that describes the anisotropic viscoelasticity is the dynamic interfacial tension, which includes the interfacial tension and dilational viscosities. Viscous dissipation due to interfacial compressibility is described by the anisotropic dilational viscosity, and it is shown to describe the Boussinesq surface fluid appropriate for Newtonian interfaces when the director is homeotropic. Three characteristic interfacial shear viscosities are defined according to whether the surface orientation is along the velocity direction, the velocity gradient, or the unit normal. In the last case the expression reduces to the interfacial shear viscosity of the Boussinesq surface fluid. The theory provides a theoretical framework to study interfacial stability, thin liquid film stability and hydrodynamics, and any other interfacial rheology phenomena.
我们建立了一种适用于可压缩向列型粘性流体界面的完整宏观理论，并用于表征界面的弹性、粘性和粘弹性材料特性。推导得出的界面应力张量表达式包含弹性和粘性分量。界面弹性应力张量的表面梯度会产生切向马兰戈尼力以及法向力。即使在平面表面，后者也可能存在，这意味着原则上静态平面界面可能会承受压力跃变。不对称的界面粘性应力张量考虑了表面向列序，并根据界面变形率和界面约当导数给出。描述各向异性粘弹性的材料函数是动态界面张力，它包括界面张力和膨胀粘度。由各向异性膨胀粘度描述的界面压缩性引起的粘性耗散，当指向矢垂直于界面时，它被证明可描述适用于牛顿界面的布辛涅斯克表面流体。根据表面取向是沿着速度方向、速度梯度还是单位法线，定义了三种特征界面剪切粘度。在最后一种情况下，表达式简化为布辛涅斯克表面流体的界面剪切粘度。该理论为研究界面稳定性、薄液膜稳定性和流体动力学以及任何其他界面流变现象提供了一个理论框架。
