the molecular diffusion coefficient

A student injects 5 mL of 20% Rhodamine solution in water (with specific gravity 1.15 g/mL) instantaneously and uniformly over the tube cross-section (𝐴𝐴 = 0.8 cm3) at the point π‘₯π‘₯ = 0 and the time 𝑑𝑑 = 0. The tube is filled with stagnant water. Assume the molecular diffusion coefficient if 𝐷𝐷 = 0.13Β·10-4 cm2/s.

β€’ What is the concentration at π‘₯π‘₯ = 0 at the time 𝑑𝑑 = 0?

β€’ What is the standard deviation of the concentration distribution 𝑑𝑑 = 1 second after injection?

β€’ Plot the maximum concentration in the tube, πΆπΆπ‘šπ‘šπ‘šπ‘šπ‘šπ‘š(𝑑𝑑), as a function of time over the interval 𝑑𝑑 = [0, 24 h].

β€’ How long does it take until the concentration over the region π‘₯π‘₯ = [-1, +1] meters can be treated as uniform? (A uniform distribution is one where the minimum concentration within a region is no less than 95% of the maximum concentration within that same region.)

BIOE2397 Homework #6

SUBMISSION FORMAT:

You will need to include the plots generated by MATLAB code into your homework document, and convert this document into a PDF. Submit your PDF and MATLAB code files in a single ZIP archive file to:

o Ms. Madeleine Lu (mlu5@uh.edu)

o Prof. Sergey Shevkoplyas (sshevkoplyas@uh.edu)

The filename must start with your last name, first name ‐‐ for example, for a student named John Doe, the filename is “Doe, John ‐ Homework 6.zip”