The role of heat-conducting walls in the measurement of heat and mass transport in transient grating experiments

Abstract

We present a two-dimensional model to account for the role of heat-conducting walls in the measurement of heat transport and Soret-effect--driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D(th, app)<D(th, s), where D(th,s) is the true thermal diffusivity of the sample. The ratio D(th, app)/D(th, s) depends on only three dimensionless parameters, d/l(s), kappa(s)/kappa(w), and D(th, s)/D(th, w). d is the grating period, l(s) the sample thickness, kappa(s) and kappa(w) the thermal conductivities of sample and wall, respectively, and D(th,w) the thermal diffusivity of the wall. If at least two measurements are performed at different d /l(s), both D(th,s) and kappa(s) can be determined. Instead of costly solving PDEs, D(th,s) can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true thermal and collective diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model.