Question

You are a Coronavirus-prevention consultant analyzing the football stadium. You are reviewing past aerial footage of a crowd rushing from the stadium onto a field after a game. You can think of the seating area as a container and the field as another container, with a boundary between. (A) If you think of this as a diffusion problem (two dimensional), how would you calculate the flux in the system? (B) Would you use Fick’s first law or Fick’s second law to describe the mass transport? Explain your reasoning. (C) If all of the people end up on the field at long times, would it be accurate to model this crowd movement as diffusion? Explain your reasoning.

Answer 1

Diffusion of net movement of anything from (atoms,ion,molecules ) from a region of higher concentration to a region of lower concentration driven by gradient in concentration.

A.Yes the above problem is a diffusion problem as the crowd is moving from stadium where the no. of people are more onto the field where the no. of people are less.

Each model of diffusion expresses the diffusion flux through concentrations, densities and their derivatives.

Flux is vector J representing the quantity and direction of transfer . The transfer of physical quantity N through a small area  

where is the inner product and   is the little-o notation.

B. I will prefer Fick's first law of diffusion to describe mass concentration as the diffusion occurs in response to a concentration gradient expressed as the change in concentration due to change in position.

c. No, it would not be accurate to model this crowd movement as diffusion because in diffusion particals move from higher concentration to lower concentration until the condition of equlibrium is achieved, that is there equal concentration on both the sides.