The Study of Magnetic Fluid Flows in a Laterally Heated Vertical Channel
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
The Study of Magnetic Fluid Flows in a Laterally Heated Vertical Channel I. N. Cherepanova,*, B. L. Smorodina, and A. S. Sidorova aPerm
State Research University, ul. Bukireva 15, Perm, 614990 Russia *e-mail: [email protected]
Received August 6, 2018; revised August 6, 2018; accepted August 15, 2018
Abstract—Convection of a stratified magnetic fluid in a laterally heated vertical channel is investigated experimentally and theoretically. The dynamics of the behavior of convective rolls, their velocity and deformation, are investigated. It is shown that the complex inhomogeneous structure of the flow is attributed to the stratification of nanoparticles in the gravitational field. On the basis of a mathematical model of convection in the Boussinesq approximation, a large series of computational experiments are carried out for various parameters of the problem: the initial distribution of nanopartciles, the Boltzmann number, the Soret parameter, and the sedimentation length. A range of parameters is found in which the numerical and experimental results are qualitatively similar. DOI: 10.1134/S1063776119020055
1. INTRODUCTION Magnetic fluids are nonconducting fluids in which solid single-domain ferromagnetic (magnetite, cobalt) particles with an average size of 10 nm, coated with surfactants, are suspended in an organic solvent (kerosene or transformer oil). Magnetic fluids belong to the class of colloidal solutions, which occupy an intermediate position between true (molecular) solutions and coarsely dispersed suspensions [1]. The impurity nanoparticles take part in thermal motion in spite of the fact that their size is an order of magnitude greater than the size of a molecule. Colloidal suspensions exhibit the phenomena of diffusion and thermal diffusion of nanoparticles. As a rule, magnetic fluids are considered as homogeneous media without regard to their multicomponent composition [2]. However, external (gravitational, magnetic, or temperature) fields may give rise to a nonuniform distribution of the impurity in a colloidal solution, which leads to convective flows, which are not observed in homogeneous fluids, such as traveling waves [3–6], flip-over oscillations [7], and complex oscillatory [8] and chaotic regimes [9–11]. The process of stratification of an isothermal colloid was theoretically studied in [12]. The characteristic setting time of the equilibrium barometric distribution of concentration is described by the expression (1) τ ≈ h2 /π2D, where h is the layer height and D is the diffusion coefficient, which can be estimated by the Einstein– Stokes formula
(2) D = kBT /6πηr, where kB is the Boltzmann constant, T is temperature, η is the dynamic viscosity of the carrier fluid, and r is the radius of nanoparticles. The characteristic value of the diffusion coefficient for a magnetic nanofluid is 10–7 cm2/s, which gives a value on the order of τ = 107 s ≈ 102 days for the setting time of the barometric distribution for a channel of height 1 cm. The experimental
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