In a manufacturing process, an organic solvent (methyl ethyl ketone, MEK) is used to dissolve a thin coating of a polymer film away from a nonporous flat surface of length 20 cm and width 10 cm, as shown in the figure (above right). The thickness of the polymer film is initially uniform at „“_a= 0.20 mm (0.02 cm). In the present process, a volumetric flow rate of 30 cm³/s of MEK liquid solvent is added to an open flat pan of length 30 cm and width 10 cm. The depth of the liquid MEK solvent in the pan is maintained at 2.0 cm. It may be assumed that the concentration of dissolved polymer in the bulk solvent is essentially zero (c_A,ˆž‰ˆ 0) even though in reality  the concentration of dissolved polymer in the solvent increases very slightly from the entrance to the exit of the pan. It may also be assumed that the change film thickness during the dissolution process does not affect the convection mass- transfer process. Let A = polymer (solute), B = MEK (liquid solvent). 

a. What are the Schmidt number and the average Sherwood number for the mass-transfer process? 

b. What is the average flux of dissolved polymer (in units of g A/cm² · s) from the surface? 

c. Plot out the local k_c,x vs. position x, for 0 < x ‰¤ L. 

d. Eventually, the polymer film will completely dissolve away from the entire surface. However, before this time the thickness of the polymer film remaining on the flat surface will not be uniform. Plot out what a plot of polymer film thickness (e) vs. position x would look like at three different times before the polymer film is completely dissolved. 

e. What are the hydrodynamic (δ) and concentration boundary- layer (δ_c) thicknesses at x = 10 cm? 

Potentially useful data: D_AB = 3.0 × 10^-6 cm²/s, the diffusion coefficient of dissolved polymer (solute A) in liquid MEK solvent at 25°C; ρ_A,solid = 1.05 g/cm³, mass density of solid polymer film material; c_As = c_A = 0.04 g/cm³, maximum solubility of dissolved polymer (solute A) in MEK solvent at 25°C; v_B = 6.0 × 10^-3 cm²/s, kinematic viscosity of liquid MEK at 25°C; ρ_B = 0.80 g/cm³, mass density of liquid MEK solvent at 25°C. 

Transcribed Image Text:

30 cm/s liquid MEK polymer film (initially 0.2 mm thick) 2 cm X = 0 width of pan = 10 cm x = L = 20 cm exiting MEK