  Exact analytical solutions are derived for the Stokes flows within
evaporating sessile drops of spherical and cylindrical cap shapes. The results
are valid for arbitrary contact angle. Solutions are obtained for arbitrary
evaporative flux distributions along the free surface as long as the flux is
bounded at the contact line. The field equations, E^4(Psi)=0 and Del^4(Phi)=0,
are solved for the spherical and cylindrical cap cases, respectively. 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<theta_c<pi, the mass flux of vapor becomes singular at the contact line. This
condition required modification when solving for the 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 present viscous flow behavior is compared to the inviscid flow behavior
previously reported. It is seen that the streamlines for viscous flow lie
farther from the substrate than the corresponding inviscid ones.
