Capillary Performance of Evaporating Flow in Micro Grooves: An Approximate Analytical Approach and Experimental Investigation

Abstract

The capillary flow along a microgroove channel was investigated both analytically and experimentally. In order to obtain insight into the phenomena, and because the governing equation had the form of a nonlinear differential equation, an analytical solution and approximate algebraic model were developed rather than using numerical methods. Approximating the governing equation as a Bernoulli differential equation resulted in an analytical solution for the radius curvature as the cube root of an exponential function. The axial variation of the radius of curvature profile as determined by this method was very similar to the numerical result as was the algebraic solution. However, the analytical model predicted the meniscus dryout location to be somewhat shorter than either the numerical results or the results from the algebraic solution. To verify the modeling results, the predictions for the axial capillary performance were compared to the results of the experimental investigation. The results of this comparison indicated that the experimentally measured wetted length was approximately 80 percent of the value predicted by the algebraic expression. Not only did the prediction for the dryout location from the algebraic equation show good agreement with the experimental data, but more importantly, the expression did not require any experimentally correlated constants. A nondimensionalized expression was developed as a function of just one parameter which consists of the Bond number, the Capillary number, and the dimensionless groove shape geometry for use in predicting the flow characteristics in this type of flow.