### Vereshchagin A.S. Фомин В.М. Зиновьев В.Н. Казанин И.В. Пак А.Ю. Лебига В.А.

## Elaborating interphase forces in heterogeneous material using linear approximation of media parameters

### Reporter: Vereshchagin A.S.

One of the promising approach for modeling of heterogeneous systems is continual approach of dynamics of multiphase media. It is developed in works of well known russian scientists as Rakhmatulin H.A., Nigmatulin R.I., Nikolaevskii V.N. etc. and is based on averaging of conservation laws over space. As a result we get conservation laws for averaged parameters of media which are similar to classical laws of fluid mechanics but with source terms describing interphase interactions (mass, momentum, energy). This method is good for mixtures with small concentrations of dispersed phase.

Usually [1-3] these terms are taken in form of solutions of classical problems of flow around sphere of viscous fluid or impirical relations from experimental data. Averaging of parameters leads to loss of local values of functions demanded for calculating interphase interaction terms. Accounting of phase geometry is made through volume ratios of phases, what makes such models inaccurate. For creating more accurate models it is necessary to know function values and their derivatives of high orders in the averaging area. In this work on the basis of linear approximation of parameters of mixture it is shown how it can be achieved and what relations are needed to be added to classical model of ideal and viscous gas and dispersed phase of spherical particles.

[1] Nigmatulin R 1987 Dynamics of multiphase media. Part 1. (M.:Nauka)

[2] Vereshchagin A and Fomin V M 2015 Journal of Applied Mechanics and Technical Physics 56 737–749

[3] Whitaker S 1999 The Method of Volume Averaging (Springer Science+Business Media Dordrecht)

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