Answered step by step
Verified Expert Solution
Question
1 Approved Answer
In this problem we consider a tissue in the form of a sphere consisting of a matrix of cells in which molecular oxygen is diffusing
In this problem we consider a tissue in the form of a sphere consisting of a
matrix of cells in which molecular oxygen is diffusing from outside the tissue
surface where the concentration is maintained as a constant As oxygen
diffuses through the matrix, the cells use the oxygen in various metabolic
pathways that we model as an overall "zeroth" order chemical reaction ie the
rate is independent of the concentration of the oxygen Thus the mass balance
of the oxygen, assuming spherical symmetry so there is only a flux of oxygen in
only the direction which is given in spherical coordinates by:
The radius of the tissue mass is given by ro We can distinguish two cases. In
the first, the concentration of oxygen throughout the sphere is greater than
zero; particularly at the core the concentration is greater than zero.
Determine the concentration distribution. In the second case, because of the
reaction there is a central region in which there is no oxygen; due to the zeroth
order reaction, all the oxygen is consumed. The radius of the inner core is
denoted by Find this radius and a criterion for when the oxygen free zone will
exist.
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started