Polydisperse Systems

All information necessary to calculate the interactions for polydisperse systems are stored in the struct twobody_f for each pair characterized by the size ratio $\lambda := a_2 / a_1$.

• calc_lub_[f,ft,fts]_2b_poly() in f.c, ft.c, fts.c:
  calculate lubrication forces (and torques and stresslets) by

  $$\left[ \begin{array}{c} \bm{F}^{(1)} \\ \bm{F}^{(2)} \end{array} ... ...cdot \left[ \begin{array}{c} \bm{U}^{(1)} \\ \bm{U}^{(2)} \end{array} \right] ,$$ (6.6)

  
  
  for particles i1 and i2 at x1[3] and x2[3], respectively. This calculation is done in the SD scaling, achieved by the function scalars_res_poly_scale_SD(). The function scalars_lub_poly_full() is called to obtain the scalar functions of the lubrication matrix.
• scalars_lub_poly_full() in minv-poly.c:
  calculate scalar functions of lubrication matrix defined by

  $$\bm{L}_{\text{2B}} := \bm{R}^{\text{exact}}_{\text{2B}} - \left( \bm{M}^{\infty}_{\text{2B}} \right)^{-1} .$$ (6.7)

  
  
  In this routine, the functions twobody_scalars_res() and scalars_minv_[f,ft,fts]_poly() are called. The former is called twice to obtain scalar functions for $12$- and $21$-pairs in $\bm{R}^{\text{exact}}_{\text{2B}}$, and the latter is once for $(\bm{M}^{\infty}_{\text{2B}})^{-1}$. The scalar functions are in the dimensional form.
• twobody_scalars_res() in twobody.c:
  This routine handles whether lubrication form is used for the exact solution (to improve the convergence), and the scaling of the result scalar functions.