An analytical solution of the Fredholm linear integral equation of the second kind for the one-particle distribution function of a liquid near a solid molecularly smooth surface is obtained. The one-particle distribution function describes the change in local density for all distances of particles from the surface. The solution is obtained in the particular case of a molecular system of solid spheres. The kernel and right-hand side of the Fredholm equation are calculated in the Percus–Yevick approximation. The interaction of particles with the surface is treated in elastic approximation.
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Agrafonov et al. (2023) studied this question.
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