In the coating process in Fig. P7.11 a liquid is extruded through a slot in a die onto a solid sheet moving horizontally at velocity V. The pressure at the slot exit is P₁ and there is a constant gap thickness H between the die and sheet. Within which an immersed substrate is withdrawn through a gas–liquid interface. Problem 1.6 focused on what occurs near the surface of a pool of liquid, as a solid sheet is pulled upward at a constant velocity V. The concern now is what happens farther up. Above a certain height, the liquid film on the sheet will achieve a constant thickness H, as shown in Fig. P7.10. At even larger x, suppose that evaporation or reaction causes the film to solidify. It is desired to predict the thickness H_∞ of the solid film.

Data from problem 1.6

(a) Assuming that the air pressure is constant at P₀ and that viscous stresses in the gas are negligible, determine the local liquid velocity v_x(y) and the mean liquid velocity U.

(b) If the liquid and solid densities are the same, how is H_∞/H related to H, V, and the liquid properties?

(c) Use the result of part (b) and Eq. (P1.6-2) to evaluate H_∞/H for the two extremes of the capillary number, Ca → 0 and Ca → ∞.

Transcribed Image Text:

1.6. Dip coating Various industrial processes require that a flat sheet be coated with a uniform liquid film. Dip coating is a procedure in which an immersed substrate is withdrawn through a liquid-gas interface. In the process in Fig. P1.6, in which a substrate is pulled upward at a constant velocity V, the coating achieves a uniform thickness H at a certain height above the liquid. It is desired to predict H from V and the liquid properties (u, p, and y). V Solid H Air Liquid