The time it takes for the liquid to pass through the walls can be calculated using the Washburn equation:
t = (ηLr^2)/(4σcosθ)
where:
- η is the viscosity of the liquid
- L is the average length of the pores
- r is the average pore radius
- σ is the surface tension
- θ is the contact angle between the liquid and the mold wall
Assuming perfect wetting, the contact angle is 0°, so cosθ = 1. Substituting the given values, we get:
t = (1.01 x 10^-3 Pa.s x 3.2 x 10^-2 m x (0.5 x 10^-3 m)^2)/(4 x 73 x 10^-3 N/m x 1)
t = 2.03 x 10^-4 s
Therefore, it takes approximately 0.203 ms for the liquid to pass through the walls.
The flow rate of liquid through each pore can be calculated using Poiseuille's law:
Q = πr^4ΔP/(8ηL)
where:
- Q is the flow rate
- ΔP is the pressure difference across the wall
Assuming the pressure difference across the wall is 1 atm, or 101325 Pa, we get:
Q = π(0.5 x 10^-3 m)^4 x 101325 Pa/(8 x 1.01 x 10^-3 Pa.s x 3.2 x 10^-2 m)
Q = 1.13 x 10^-10 m^3/s
Therefore, the flow rate of liquid through each pore is approximately 1.13 x 10^-10 m^3/s.