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 𝑥𝑥 = 0 and the time 𝑡𝑡 = 0. The tube is filled with stagnant water. Assume the molecular diffusion coefficient if 𝐷𝐷 = 0.13·10-4 cm2/s.

• What is the concentration at 𝑥𝑥 = 0 at the time 𝑡𝑡 = 0?

• What is the standard deviation of the concentration distribution 𝑡𝑡 = 1 second after injection?

• Plot the maximum concentration in the tube, 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚(𝑡𝑡), as a function of time over the interval 𝑡𝑡 = [0, 24 h].

• How long does it take until the concentration over the region 𝑥𝑥 = [-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”