The evaporation of a sessile droplet with a pinned contact line is investigated experimentally, by analytic theory and by computation using the finite element method (FEM). Because of the low value of R2Dtf = cv(l - H)/p = 1.4 x 10-5, where R is the contact-line radius, D is the water vapor diffusivity, cv is the saturated water vapor concentration, H is the relative humidity, and p is the liquid water density, the evaporation can be considered as a quasi-steady-state process. Hence, the vapor concentration distribution above the droplet satisfies the Laplace equation but with a time-varying droplet surface. It is found both theoretically and experimentally that the net evaporation rate from the droplet remains almost constant with time for a small initial contact angle (O < 40º), even though the evaporation flux becomes more strongly singular at the edge of the droplet as the contact angle decreases during evaporation. We also measured the critical contact angle at which the contact line starts to recede and found that it is about 2-4º for clean water on glass. Finally, we compare the results obtained by our FEM analysis with an analytical solution and derive a very simple approximate evaporation rate expression m(t) = -πRD(1 - H)cv(0.2702 + 1.30), which agrees with the theoretical results presented by Lebedev [Lebedev, N. N. Special Functions and Their Application; Prentice Hall: Englewood Cliffs, New Jersey, 1965 and Picknett and Bexon [Picknett, R. G.; Bexon, R. J. Colloid Interface Sci. 1977, 61, 366] for any initial contact angle 0 between 0 and π/2 with 0 in radians. The approximate expression is also compared with droplet evaporation data from the literature, and good agreement is found without any parameter fitting.
Hu, H., Larson, R.G., Evaporation of a Sessile Droplet on a Substrate, J. Phys. Chem., B., American Chemical Society, Columbus, OH, Vol. 106, pp. 1334-1344, 2002.