Lee Sungho, Ohsaka Kenichi, Rednikov Alexei, Sadhal Satwindar Singh
Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089-1453, USA.
Ann N Y Acad Sci. 2006 Sep;1077:75-95. doi: 10.1196/annals.1362.060.
The purpose of the current research program is to develop techniques for noncontact measurement of thermophysical properties of highly viscous liquids. The application would be for undercooled liquids that remain liquid even below the freezing point when suspended without a container. The approach being used here consists of carrying out thermocapillary flow and temperature measurements in a horizontally levitated, laser-heated thin glycerin disk. In a levitated state, the disk is flattened by an intense acoustic field. Such a disk has the advantage of a relatively low gravitational potential over the thickness, thus mitigating the buoyancy effects, and helping isolate the thermocapillary-driven flows. For the purpose of predicting the thermal properties from these measurements, it is necessary to develop a theoretical model of the thermal processes. Such a model has been developed, and, on the basis of the observed shape, the thickness is taken to be a minimum at the center with a gentle parabolic profile at both the top and the bottom surfaces. This minimum thickness is much smaller than the radius of disk drop and the ratio of thickness to radius becomes much less than unity. It is heated by laser beam in normal direction to the edge. A general three-dimensional momentum equation is transformed into a two-variable vorticity equation. For the highly viscous liquid, a few millimeters in size, Stokes equations adequately describe the flow. Additional approximations are made by considering average flow properties over the disk thickness in a manner similar to lubrication theory. In the same way, the three-dimensional energy equation is averaged over the disk thickness. With convection boundary condition at the surfaces, we integrate a general three-dimensional energy equation to get an averaged two-dimensional energy equation that has convection terms, conduction terms, and additional source terms corresponding to a Biot number. A finite-difference numerical approach is used to solve these steady-state governing equations in the cylindrical coordinate system. The calculations yield the temperature distribution and the thermally driven flow field. These results have been used to formulate a model that, in conjunction with experiments, has enabled the development of a method for the noncontact thermophysical property measurement of liquids.
当前研究项目的目的是开发用于非接触测量高粘性液体热物理性质的技术。其应用对象是过冷液体，这种液体在无容器悬浮时，即使低于冰点仍保持液态。此处所采用的方法是在水平悬浮、激光加热的薄甘油盘内进行热毛细流动和温度测量。在悬浮状态下，圆盘被强声场扁平化。这样的圆盘具有厚度方向上引力势能相对较低的优势，从而减轻了浮力效应，并有助于隔离热毛细驱动的流动。为了从这些测量结果预测热性质，有必要开发热过程的理论模型。这样的模型已经开发出来，并且根据观察到的形状，圆盘厚度在中心处最小，顶面和底面均呈平缓的抛物线轮廓。这个最小厚度远小于圆盘液滴的半径，厚度与半径之比远小于1。它由垂直于边缘的激光束加热。一般的三维动量方程被转化为双变量涡度方程。对于几毫米大小的高粘性液体，斯托克斯方程足以描述其流动。通过以类似于润滑理论的方式考虑圆盘厚度上的平均流动特性，进行了额外的近似。同样，三维能量方程在圆盘厚度上进行平均。在表面采用对流边界条件，我们对一般的三维能量方程进行积分，得到一个平均的二维能量方程，该方程具有对流项、传导项以及对应于毕奥数的附加源项。采用有限差分数值方法在圆柱坐标系中求解这些稳态控制方程。计算得出温度分布和热驱动流场。这些结果已被用于构建一个模型，该模型与实验相结合，使得开发一种用于液体非接触热物理性质测量的方法成为可能。
