An Analytical Model of External Streaming and Heat Transfer for a Levitated Flattened Liquid Drop

Abstract

We present here the heat transfer and fluid flow analysis of an acoustically levitated flattened disk-shaped liquid drop. This work arises due to an interest in the non-contact measurement of the thermophysical properties of liquids. Such techniques have application to liquids in the undercooled state, i.e., the situation when a liquid stays in a fluidic state even when the temperature falls below the normal freezing point. This can happen when, for example, a liquid sample is held in a levitated state. Since such states are easily disrupted by measurement probes, non-contact methods are needed. We have employed a technique involving the use of acoustically levitated samples of the liquid. A thermal stimulus in the form of laser-heating causes thermocapillary motion with flow characteristics depending on the thermophysical properties of the liquid. In a gravity field, buoyancy is disruptive to this thermocapillary flow, masking it with the dominant natural convection. As one approach to minimizing the effects of buoyancy, the drop was flattened (by intense acoustic pressure) in the form of a horizontal disk, about 0.5 mm thick. As a result, with very little gravitational potential, with most of the buoyant flow suppressed, thermocapillary flow remained the dominant form of fluid motion within the drop. This flow field is visualizable and subsequent analysis for the inverse problem of the thermal property can be conducted. This calls for numerical calculations involving a heat transfer model for the flattened drop. With the presence of an acoustic field, the heat-transfer analysis requires information about the corresponding Biot number. In the presence of a high-frequency acoustic field, the steady streaming originates in a thin shear-wave layer, known as the Stokes layer, at a surface of the drop. The streaming develops into the main fluid, and is referred to as the outer streaming. Since the Stokes layer is asymptotically thin in comparison to the length scale of the problem, the outer streaming formally appears to be caused by an effective slip velocity at the boundary. The presence of the thin Stokes layer, and the slip condition at the interface, changes the character of the heat transfer mechanism which is inherently different from the traditional boundary layer. The current analysis consists of a detailed semi-analytical calculation of the flow field and the heat transfer characteristics of a levitated drop in the presence of an acoustic field.