TY - JOUR

T1 - Diffusion of a vortex and conservation of moment of momentum in dynamics of nonpolar fluids. PMM vol.34, n≗2, 1970, pp. 318-323

AU - Nigmatulin, R. I.

AU - Nikolaevskii, V. N.

PY - 1970

Y1 - 1970

N2 - We show that the law of consevation of angular momentum in a flow of an incompressible Stokes fluid can, in a particular case, be reduced to the equation of vortex diffusion. We perform the analysis using two different representations, the Euclerian and the Lagrangian, of the kinetic moment of a fluid particle. We discuss the relevant concepts of the moments of inertia and give an equation for the rate of change of the Lagrangian moment of inertia of a fluid particle. For the classical (nonpolar) media the law of conservation of the angular momentum can only lead to the condition of symmetry of the stress tensor [1], and nontrivial results can be expected only for the media with microstructure [2]. However when we consider the volumes whose characteristic dimensions are comparable with the scale of the velocity gradient field, then the balance of the angular momentum will necessarily include the kinetic moment and the mean vortical motion. Moreover it appears, that in the case of a nonpolar (e.g. Stokes') fluid, the first terms of the Taylor expansion of the kinetic moment of a particle which are not identically equal to zero, are defined by a vortex motion. We shall show that the kinetic moment of the elementary (from the point of view of the continuum mechanics) volume of the conventional viscous fluid must be taken into account in the study of flows of suspensions containing rotating fluidized particles [3]. This is true particularly in the case of anisotropic turbulent flows [4].

AB - We show that the law of consevation of angular momentum in a flow of an incompressible Stokes fluid can, in a particular case, be reduced to the equation of vortex diffusion. We perform the analysis using two different representations, the Euclerian and the Lagrangian, of the kinetic moment of a fluid particle. We discuss the relevant concepts of the moments of inertia and give an equation for the rate of change of the Lagrangian moment of inertia of a fluid particle. For the classical (nonpolar) media the law of conservation of the angular momentum can only lead to the condition of symmetry of the stress tensor [1], and nontrivial results can be expected only for the media with microstructure [2]. However when we consider the volumes whose characteristic dimensions are comparable with the scale of the velocity gradient field, then the balance of the angular momentum will necessarily include the kinetic moment and the mean vortical motion. Moreover it appears, that in the case of a nonpolar (e.g. Stokes') fluid, the first terms of the Taylor expansion of the kinetic moment of a particle which are not identically equal to zero, are defined by a vortex motion. We shall show that the kinetic moment of the elementary (from the point of view of the continuum mechanics) volume of the conventional viscous fluid must be taken into account in the study of flows of suspensions containing rotating fluidized particles [3]. This is true particularly in the case of anisotropic turbulent flows [4].

UR - http://www.scopus.com/inward/record.url?scp=49849113943&partnerID=8YFLogxK

U2 - 10.1016/0021-8928(70)90143-7

DO - 10.1016/0021-8928(70)90143-7

M3 - Article

AN - SCOPUS:49849113943

VL - 34

SP - 297

EP - 302

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 2

ER -