Nonlinear effects of thermophoresis of a single particle in a medium with a temperature gradient

Aim. Development of a microscopic model of thermophoresis of a single particle that goes beyond the linear approximation and takes into account significant nonlinear effects that occur under conditions of strong temperature gradients.

Methodology. The methods of stochastic thermodynamics were applied and the modified Langevin equation with temperature-dependent parameters was used, which made it possible to analytically derive the expression for the thermophoretic velocity taking into account quadratic corrections for the temperature gradient.

Results. The results obtained demonstrate qualitatively new features of thermophoretic drift: the possibility of inverting the direction of particle motion when critical values of the temperature gradient are reached, significant deviations from the predictions of linear theory in the field of strong temperature field inhomogeneities, as well as a pronounced dependence of the observed effects on the parameters of the medium. The analysis of fluctuation-dissipative ratios established a connection between the microscopic characteristics of the system and the macroscopic manifestations of thermophoresis.

Research implications. lie in a significant expansion of the fundamental concepts of thermophoretic transfer mechanisms, which for the first time systematically takes into account second-order nonlinear effects. From a practical point of view, the developed model creates the basis for new methods for controlling particle motion in microfluidic devices and nanotechnology applications, and also allows us to explain a number of experimentally observed anomalies in the behavior of colloidal systems and biological objects in inhomogeneous temperature fields.

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