Velocity fluctuations in a steadily sheared model foam

Numerical simulations are conducted to calculate velocity fluctuations in a simple two-dimensional model of foam under steady shear. The width of the velocity distribution increases sublinearly with the shear rate, indicating that velocity fluctuations are large compared to the average flow at low shear rates (stick-slip flow) and small compared to the average flow at large shear rates. Several quantities reveal a crossover in behavior at a characteristic strain rate ̇ \.γₓ, given by the yield strain divided by the duration of a bubble rearrangement event. For strain rates above ̇ \.γₓ, the velocity correlations decay exponentially in space and time, and the velocity distribution is a Gaussian. For strain rates below ̇ \.γₓ, the velocity correlations decay as stretched exponentials in space and time, and the velocity distribution is broader than a Gaussian.