# Bio transport Homework

1. A drug has an equilibrium solubility in water of 0.0025 g cm^-3. The diffusivity of the drug in water is 0.9 x 10^-5 cm2/sec. The drug is made into particles that have a radius of 0.1 cm and these particles have a density of 1.27 g/cm^3. These particles are all of the same size and are gently mixed in water in a stirred vessel. Estimate the length of time in hours (hrs) that it will take for these drug particles to completely dissolve. You can assume that the vessel volume is so large that the concentration of the drug in the bulk liquid is very small in comparison to the drug solubility. Also since the particles are all the same size, the time to dissolve is the same for all the particles. So we can focus on just one particle and write an unsteady mass balance on that particle, i.e., d(ρV)/dt = – 4πR^2 km (Csurface – 0) , where V is the particle volume and equals 4/3 πR^3 .

2. A particular drug is a solid at 300 K and is soluble in water. The equilibrium solubility of

the drug in water is 0.005 g cm–3. The MW of the drug is 600. One hundred grams of the

drug is made into particles that are 0.2 cm in diameter. The density of the drug particles

is 1.05 g cm–3. These particles are then very gently mixed in a stirred vessel containing

100 L of water. After 10 min of mixing, estimate how many grams of the drug have dissolved

into the water.

3. A flat plate coated with a layer of a volatile organic material is exposed to a parallel flow

of air at 20°C with a free stream air velocity of 5 m sec–1. The length of the flat plate in

the direction of flow is 0.5 m. Estimate how long it will take for the average thickness

of the volatile organic layer to decrease by 1 mm. The saturation concentration of the

organic material in air at these conditions is 1.85 × 10–9 mol cm–3 and its diffusivity in air is

0.068 cm2 sec–1. The density of the volatile organic material as a solid is 1.21 g cm–3 and its

MW is 140.2. Also, the kinematic viscosity of air at these conditions is 0.155 cm2 sec–1.

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