Analytical and numerical study of fluid flow and particle deposition inside an evaporating sessile drop
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Exact analytical solutions are derived for the inviscid and Stokes flows within evaporating sessile drops. While spherical cap geometry is considered for the inviscid flow, Stokes flow problem is solved for both spherical and cylindrical cap geometries. The results are valid for all contact angles. Solutions are obtained for arbitrary evaporative flux distributions along the free surface with the exception that the flux has to be bounded at the contact line when Stokes flow is considered. Specific results and computations are presented for evaporation corresponding to uniform flux and to purely diffusive gas phase transport into an infinite ambient. Wetting and non-wetting contact angles are considered with the flow patterns in each case being illustrated. For the spherical cap with evaporation controlled by vapor phase diffusion, when the contact angle lies in the range 0 ≤ [straight theta] c < π / 2, the mass flux of vapor becomes singular at the contact line. This condition requires modification when solving for the viscous liquid phase transport. Droplets in all of the above categories are considered for the following two cases: the contact lines are either pinned or free to move during evaporation. The viscous flow behavior is compared to the inviscid counterpart. It is seen that the streamlines for viscous flow lie farther from the substrate than the corresponding inviscid ones. In addition to the flow fields, for colloidal drops the deposition patterns of the suspended particles are determined as the liquid evaporates. Results are obtained for diffusive evaporative flux and for various contact angles. Using the Lagrangian approach to track particle movements, it is observed that the majority of particles intersect the free surface as it recedes due to evaporation. This mechanism of particle "capture" by the free surface is found to play the major role in establishing the pattern of particle deposition. The theoretical results are found to agree favorably with available experimental data.