This article is cited in 2 papers

Mathematical Modeling, Numerical Methods and Software Complexes

Numerical study of mass transfer in drop and film systems using a regularized finite difference scheme in evaporative lithography

K. S. Kolegov^ab, A. I. Lobanov<sup>c

a</sup> Astrakhan State University, Astrakhan, 414056, Russian Federation
^b Volga State University of Water Transport (Caspian Institute of Sea and River Transport the Branch of VSUWT), Astrakhan, 414000, Russian Federation
^c Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, 141700, Russian Federation

Abstract: Mass transfer in drying drops and films is interesting with practical point of view, since it is used in problems of evaporative lithography. Compensatory flows arise when conditions of nonuniform evaporation from the surface of the liquid layer are created and move colloidal particles in the region of fast evaporation. This makes it possible to obtain micro- and nanostructures of the required shape on a solid surface. Nonstationary model of mass transfer in drops and films is described in this paper. Feature of the model is to jointly take into account viscous, gravitational and capillary forces. To solve the unstable discrete problem on drying drop (film), a regularized finite difference scheme is proposed. A computer algorithm is developed on the basis of this scheme. We present a way of obtaining ring structures by using evaporative lithography method that based on the results of the computational experiments.

Keywords: mass transfer, drops, films, evaporative lithography.

UDC: 517.958:531.32

MSC: 76T20, 76R99, 74M25, 82D80

Received: January 10, 2018
Revised: May 15, 2018
Accepted: June 11, 2018
First online: June 27, 2018

DOI: 10.14498/vsgtu1601

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