CAPILLARY PERFORMANCE OF EVAPORATING FLOW IN MICRO GROOVES - AN ANALYTICAL APPROACH FOR VERY SMALL TILT ANGLES

The axial flow of an evaporating thin film through a V-shaped micro ch annel was investigated for the case of a grooved plate inclined with a very small tilt angle. For this problem, the addition of the gravity term caused by the tilt angle alters the form of the governing equatio n from linear to nonlinear. Because the effect of the tilt angle is ve ry small, a perturbation method was applied to obtain a first order pe rturbation solution of R = R-0 + epsilon R-1, where R-0 is the undistu rbed solution of a horizontally placed plate, and R-1 is the disturbed solution caused by the tilt angle. A generalized graph of the nondime nsional radius of curvature as a function of the nondimensionalized ax ial length was obtained. The perturbation parameter, epsilon, was expr essed as a function of five nondimensional parameters. The results ind icate that when the geometry is fixed, the effects of the Bond number and Capillary number are dominant. In addition, it was found that epsi lon is inversely proportional to the square root of the Capillary numb er. This indicates that the perturbation method is applicable and accu rate, even for the cae of somewhat larger tilt angles (where the initi al applicability of perturbation appears to be violated), if a suffici ently large heat flux is applied.