**MSC2010** 76W05, 76D07, 70F05, 35Q35

### Pair-wise MHD-interaction of rigid spheres in longitudinal creeping flow

#### I. P. Boriskina^{1}, A. O. Syromyasov^{2}

Annotation | Authors describe and study the mathematical model of two identical rigid spheres immersed in highly viscous fluid with magnetic field acting in it. At infinite distance from suspended particles the flow and the field are uniform. The hypothesis that bulk currents are weak allows to split magnetic and hydrodynamic interactions of the spheres. Distribution of magnetic field is obtained for arbitrary orientation of undisturbed field with respect to line going through the spheres' centers and is written in the form of multipole expansion. This expression is used to calculate magnetic force acting on both particles. Together with known expressions for hydrodynamic forces this result may be applied in study of particle dynamics in uniform flow of viscous magnetic fluid. In the paper particular case of field and flow being parallel to line of centers is examined in more detail. The opportunity of particles' coagulation in such flow is discussed. |
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Keywords | viscous fluid, Stokes equation, creeping flow, suspended particles, magnetic fluid, hydrodynamic interaction, coagulation |

^{1}**Irina P. Boriskina**, Associate Professor, Department of Calculus, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0003-3536-5838, irinaboriskina@mail.ru

^{2}**Aleksei O. Syromyasov**, Associate Professor, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics, National Research Mordovia State University (68 Bolshevistskaya Str., Saransk 430005, Republic of Mordovia, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6520-0204, syal1@yandex.ru

**Citation**: I. P. Boriskina, A. O. Syromyasov, "[Pair-wise MHD-interaction of rigid spheres in longitudinal creeping flow]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,21:1 (2019) 78–88 (In Russian)

**DOI** 10.15507/2079-6900.21.201901.78-88