The electrostriction mechanism of beam self-focusing in nanofluids is theoretically investigated. An analytical solution of the diffusion equation, which describes the dynamics of particles in nanofluids, was obtained and studied. Explicit expressions for the nonlinear part of the refractive index and concentration lens focal length are presented. It is shown that there is a limit on the radiation intensity associated with the physical and hydrodynamic characteristics of the phenomena in these processes. 1. Introduction Nanoparticles are being increasingly adopted in new and different areas of science and technology [1–4]. Colloidal suspensions that contain nanoparticles, also known as nanofluids, have found a variety of important applications in modern technologies [5]. For example, magnetic fluids are largely used for polishing optical components [6, 7], suspensions of silica particles in liquid crystals have exhibited extraordinary capabilities for optical storage [8, 9], and artificial media with a high optical nonlinearity were obtained in colloids of submicrometer-size particles in liquids [10–13]. As shown in recent studies [14–21], the liquid-phase environment of dispersed nanoparticles of wide bandgap semiconductors or insulators is very effective for a number of nonlinear optical effects. But the physical mechanisms involved, particularly with nonlinear optical processes in such media, are not entirely clear and require further study. When placed in an electromagnetic field, particles in a microheterogeneous medium, with components that have different refractive indices, are subject to electrostrictive forces that could lead to the appearance of concentration flows [21–23]. Depending on the sign of the polarizability, these microparticles can be pulled in or pushed out of high electric field areas. At the same time that this electrostriction flow phenomenon occurs, thermal diffusion due to the temperature gradient [23] also occurs, but we do not consider thermal effects here. The concentration dynamics of colloidal particles in a periodic light field have been theoretically investigated in [24, 25], and similar problems within the small-perturbation approximation of the concentration were studied in [26, 27]. In this paper, the restrictions of this approximation are removed. Here, using the exact solution of the transformed diffusion equation for particles in the field of a light wave, we explore the dynamics of the particle concentration. The results allow us to find an explicit expression for the nonlinear part of the refractive index and
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