Yy. Su, THE STABILITY OF SUPERPOSED POLYMERIC FLUIDS FLOWING DOWN AN INCLINEDPLANE AND ITS APPLICATION TO COATING PROCESSES, Polymer-plastics technology and engineering, 34(2), 1995, pp. 243-269
A mathematical analysis has been performed to investigate the combined
effects of viscosity and elasticity on the interfacial and the surfac
e stabilities of two superposed Oldroyd-B fluids flowing down an incli
ned plane. Our results indicate that arranging the less viscous and mo
re elastic liquid as the skin layer is helpful in avoiding the occurre
nce of interfacial waves. For the stability of free surface, it is fou
nd that the elasticity in each layer is always destabilizing free surf
ace waves. However, this destabilization can be lessened by designing
the more viscous liquid as the skin layer. In addition, the effect of
increasing Reynolds number on the interface and the free surface is in
vestigated. It is shown that increasing Reynolds number can stabilize
or destabilize the interface, depending on the parametric space of the
now system. However, free surface is always destabilized by an increa
se in Reynolds number. In general, our analysis indicates that under c
ertain physical conditions (i.e., viscosity and elasticity ratios) and
geometric conditions (i.e., depth ratio), stable operations in the co
ating process can be attained.