Tissue engineering is an engineering field focused on the development of living tissues. Bioengineering

reactors include scaffolds for tissue growth so that mature tissues can eventually be transplanted into the

body. Healthy tissue requires oxygen to stay alive and the mass transport of oxygen to the growing

tissues is an important design consideration. A potential system is shown below.

A bundle of thin tubes are passed longitudinally through an area designed for tissue growth. The tubes

provide a scaffold to support tissue growth as well as a means for supplying oxygen. Pure oxygen flows

through the tubes and the concentration of oxygen in tissues is limited by its solubility. The maximum

solubility of oxygen in tissue is approximately $0\mathrm{.}032g\frac{O_2}{k}g$ water $(0\mathrm{.}001M).$ The tubes are spaced to

provide the tissue space with a concentration of at least $0\mathrm{.}015g\frac{O_2}{k}g$ water.

Consider the oxygen delivery from a single tube. The tube has a diameter of $50m$ and length of $100cm.$

The concentration of oxygen is $0\mathrm{.}015g\frac{O_2}{k}g$ water $100m$ away from the surface of the tube. The

diffusion coefficient of oxygen is $1\mathrm{.}87{10}^{-5}c\frac{m^2}{sec}.$

A$)$ State the differential mass balance for diffusion through a cylinder and solve to find the concentration

profile in the tissue surrounding a tube.

B$)$ Find the flux into the tissue.