Dimensional mobility parameter in the Giesekus model (source code)

= Dimensional mobility parameter in the Giesekus model
{title2=$b=\alpha nk_BT$}

When $\sigma=nHC-nk_BT I$ and the bead <hydrodynamic mobility matrix> is $(I+\alpha\sigma)/\zeta$, $\alpha$ has inverse-<stress> units. With $p_T=nk_BT$, $A=HC/(k_BT)$ 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.