Pair correlation function of charge-stabilized colloidal systems under sheared conditions

The pair correlation function of charge stabilized colloidal particles under strongly sheared conditions is studied using the analytical intermediate asymptotics method recently developed in [L. Banetta and A. Zaccone, Phys. Rev. E 99, 052606 (2019)] to solve the steady-state Smoluchowski equation for medium to high values of the P\'eclet number; the analytical theory works for dilute conditions. A rich physical behaviour is unveiled for the pair correlation function of colloids interacting via the repulsive Yukawa (or Debye-H\"uckel) potential, in both the extensional and compressional sectors of the solid angle. In the compression sector, a peak near contact is due to the advecting action of the flow and decreases upon increasing the coupling strength parameter $\Gamma$ of the Yukawa potential. Upon increasing the screening (Debye) length $\kappa^{-1}$, a secondary peak shows up, at a larger separation distance, slightly less than the Debye length. While this secondary peak grows, the primary peak near contact decreases. The secondary peak is attributed to the competition between the advecting (attractive-like) action of the flow in the compressions sector, and the repulsion due to the electrostatics. In the extensional sectors, a depletion layer (where the pair-correlation function is identically zero) near contact is predicted, the width of which increases upon increasing either $\Gamma$ or $\kappa^{-1}$.