论文标题
可变粘度流的薄间隙平均：应用于热雾指法
Thin-gap averaging of variable-viscosity flows: application to thermoviscous fingering
论文作者
论文摘要
使用加权残差积分边界层（WRIBL）方法的一致平均技术通过薄间隙几何形状提出，其中流体的粘度在整个间隙上有所不同。在这种情况下，流动具有非促抛物性的跨隙速度曲线 - 这种效果被常规用于此类Hele-Shaw流的Darcy模型所忽略。 WRIBL技术系统地解释了粘度的跨差异变化，并产生了间隙平均流体流量的减少顺序。作为测试案例，我们考虑了具有依赖温度的粘度的流体，并分析了先前研究的热疗指法的问题：流经冷壁的热液流经冰冷的几何形状，冷壁自发地形成了低粘度的通道，热流体，热液，由高粘液液的区域隔离，冷液。假定冷墙的温度是恒定的，这种情况模仿了岩浆通过地壳中的裂缝的向上流，或者沿流动方向沿线性变化。 In both cases, the predictions of the WRIBL model, regarding the multiplicity of uniform steady flow states and their linear stability, are compared with that of the hitherto used, ad hoc, Darcy model (Helfrich, J. Fluid Mech., vol. 305, 1995, pp. 219-238), as well as with calculations of the full three-dimensional governing equations (Wylie and Lister, J. Fluid Mech., vol. 305，1995，第239-261页）。尽管结果在质上相似，但发现WRIBL模型比Darcy模型更准确。平均方法以一般方式呈现，以促进其在其他物理情况下的应用，例如，粘度取决于溶液/悬浮液中的溶质/颗粒浓度。
A consistent averaging technique, using the weighted residual integral boundary layer (WRIBL) method, is presented for flow through a thin-gap geometry wherein the fluid's viscosity varies across the gap. In such situations, the flow has a non-parabolic cross-gap velocity profile -- an effect that is ignored by Darcy models conventionally used for such Hele-Shaw flows. The WRIBL technique systematically accounts for the cross-gap variation of viscosity and yields reduced-order equations for the gap-averaged fluid flow rate. As a test case, we consider a fluid with a temperature-dependent viscosity and analyse the previously-studied problem of thermoviscous fingering: a hot fluid flowing through a Hele-Shaw geometry with cold walls spontaneously forms channels of low-viscosity, hot fluid, separated by regions of high-viscosity, cold fluid. The temperature of the cold walls is assumed either to be constant, a scenario that mimics the upward flow of magma through fissures in the Earth's crust, or to vary linearly along the direction of flow. In both cases, the predictions of the WRIBL model, regarding the multiplicity of uniform steady flow states and their linear stability, are compared with that of the hitherto used, ad hoc, Darcy model (Helfrich, J. Fluid Mech., vol. 305, 1995, pp. 219-238), as well as with calculations of the full three-dimensional governing equations (Wylie and Lister, J. Fluid Mech., vol. 305, 1995, pp. 239-261). Though the results are qualitatively similar, the WRIBL model is found to be much more accurate than the Darcy model. The averaging method is presented in a general manner to facilitate its application to other physical situations where, for example, the viscosity depends on solute/particle concentration in a solution/suspension.
