The capillary number is given by:
Ca = (mu)U/gamma = rhonuU/ gamma
mu -> dynamic viscosity
U -> velocity
nu -> kinematic viscosity
rho -> density
gamma -> interfacial tension
I used the fluid water and with a certain width in third direction. This gave me water’s area mass density(in kg/m^2) as density(in kg/m^3) * width. With proper choice of length and mass scaling factors, I calculated area mass density in LBM = 1.0.
I want to calculate the velocity U for given capillary number in LBM units.
Since my simulation is 2D, my LBM density is area-mass density while the density in the formula of Ca is volume-mass density. I don’t know which value to plug in rho. (whether area mass density = 1.0 or something else)