cuts, voids or interior walls) but are not considered in this paper. Throughout this work the largest and smallest eigenvalues of $\boldsymbol{D}$ will be denoted $\mu_{\max}$ and $\mu_{\min}$, respectively.

Furthermore, for two-body HI, $\boldsymbol{Z}_1$, $\boldsymbol{Z}_2$ are the diagonal and off-diagonal blocks respectively of the translational component of the grand resistance matrix originating in the classical theory of low Reynolds number hydrodynamics between suspended particles [@happel2012low], [@jeffrey1984calculation], related to the friction tensor by $$\begin{aligned}
\tilde{\boldsymbol{\Gamma}}_{ij}(\vec{r}^N) = \delta_{ij}\sum_{l\neq i}\boldsymbol{Z}_{1}(\vec{r}_i,\vec{r}_l)+(1-\delta_{ij})\boldsymbol{Z}_{2}(\vec{r}_i,\vec{r}_j).\end{aligned}$$

In $d = 3$ dimensions, and for the particular case $N=2$ (where $N$ is the number of particles in the system), $\bm{\Gamma}\in \mathbb{R}^{6\times 6}$ and $\bm{\Gamma}_{ij}$ may be seen as equivalent to the second-rank tensor of the translational part of the resistance matrix as found in [@jeffrey1984calculation] used to model lubrication forces. It should be noted however that the definition of those resistance matrices are formalism dependent, that is, the individual entries are scalar functions arising from the solution of Stokes equations for two-body lubrication interactions using multipole methods. Conversely, $\bm{\Gamma}_{ij}$ are general tensors, independent of the type of HI under consideration, and are therefore a more general representation of hydrodynamic phenomena of colloidal suspensions. Additionally, $\bm{\Gamma}_{ij}$ may be used to model not 