Noncontact thermophysical property measurement by levitation of a thin liquid disk

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.