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We developed an analytical theoretical method to determine the microscopicalstructure of weakly to moderately sheared colloidal suspensions in diluteconditions. The microstructure is described by the static structure factor,obtained by solving the stationary two-body Smoluchowski advection-diffusionequation. The singularly perturbed PDE problem is solved by performing anangular averaging over the extensional and compressing sectors and by therigorous application of boundary-layer theory (intermediate asymptotics). Thisallows us to expand the solution to a higher order in P\'eclet with respect toprevious methods. The scheme is independent of the type of interactionpotential. We apply it to the example of charge-stabilized colloidal particlesinteracting via the repulsive Yukawa potential and study the distortion of thestructure factor. It is predicted that the distortion is larger at smallwavevectors $k$ and its dependence on $Pe$ is a simple power law. At increasing$Pe$, the main peak of the structure factor displays a broadening and shifttowards lower $k$ in the extensional sectors, which indicates shear-inducedspreading out of particle correlations and neighbor particles locally beingdragged away from the reference one. In the compressing sectors, instead, anarrowing and shift towards high $k$ is predicted, reflecting shear-inducedordering near contact and concomitant depletion in the medium-range. An overallnarrowing of the peak is also predicted for the structure factor averaged overthe whole solid angle. Calculations are also performed for hard spheres,showing good overall agreement with experimental data. It is also shown thatthe shear-induced structure factor distortion is orders of magnitude larger forthe Yukawa repulsion than for the hard spheres.

Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate P\'eclet numbers