A cylindrical roll of cloth was soaked in a dye mixture to color it. After the dye binds to the cloth, the cloth is soaked in a well-mixed tank of solvent to remove the unbound dye. The concentration of dye in the cloth after soaking is 1000 mol/m3. This concentration is to be reduced to 10% of its starting value. If the solvent initially contains no dye and the soaking process can take no more than 20 min, what volume of solvent is required? The cloth roll is 0.1 m long and 0.04 m in diameter. The diffusivity of dye in the cloth is Ddc = 2 × 10−7 m2/s and the mass transfer coefficient in the tank is kc = 2 × 10−5 m/s. Assume the solvent is well mixed at all times (Enever, Lewandowski, and Taylor).