Question $2-$ Power Law Model

The foam rheology was measured in a pipe viscometer by $[$Tong et al$.2017].$ They use the power

law model to describe the foam rheology behavior and the apparent viscosity of the foam at

different shear rates can be calculated as:

${}_a=m{}_{wi}^{n-1}$

where ${}_a$ is the apparent viscosity of the foam and ${}_{wi}$ is the intrinsic wall shear rate.

Use their collected data in the table below to determine the two parameters $m$ and $n$ in the above

power law model. Here, we have two different foams, determine $m$ and $n$ for two foams

respectively, and discuss the difference of rheology behavior between these two foams.

Hint: Are they shear$-$thinning or shear$-$thickening fluids and why? At the same shear rate, which

foam is "thicker" and what are the possible reasons? One application offoam is to be used as the

hydraulic fracturing fluid to carry the proppant$/$sand into the formation, so if you are the

completion engineer, which foam $($Foam A or B$)$ will you choose, and why?