Dimensional mobility parameter in the Giesekus model ($b=\alpha n{k}_{B}T$)

When $\sigma =nHC-n{k}_{B}TI$ and the bead hydrodynamic mobility matrix is $(I+\alpha \sigma )/\zeta$, $\alpha$ has inverse-stress units. With $p_T=n{k}_{B}T$, $A=HC/(k_{B}T)$ and $b=\alpha p_T$, the dimensionless mobility is $M=(1-b)I+bA$. Thus $0<b<1$ and a positive-definite conformation tensor ensure a positive-definite mobility. The closed constitutive equation is $\lambda {\sigma }^{\nabla }+\sigma +\alpha {\sigma }^2=\mu (G+G^T)$, with $\lambda =\zeta /(4H)$ and $\mu =\lambda p_T$. This dimensional $\alpha$ differs from conventions in which the symbol denotes $b$ itself.