Drying of polymeric coatings often occurs under conditions where the r
elaxation time of polymer molecules is significant with respect to the
processing time scales. The nonequilibrium thermodynamic theory of Du
rning and Tabor (1986) is applied to model 1-D drying of viscoelastic
solutions with concentration-dependent physical properties. Transport
of solvent to the surface of the coating occurs by viscoelastic diffus
ion down the gradient of a diffusion potential with a relaxing nonequi
librium contribution. Galerkin's method with finite-element basis func
tions and a differential/algebraic equation system solver enable effic
ient solution of this stiff nonlinear model. Predictions show that ela
sticity enhances diffusion within the coating. At high Deborah numbers
, however, a fall in the surface activity slows the rare of desorption
. The coating thickness after a specified time under fixed total drivi
ng force is the smallest at intermediate Deborah numbers, showing that
a small amount of viscoelasticity actually aids in drying. This can b
e interpreted as a skinning effect.