|Wall effects on Reiner-Rivlin liquid spheroid
|Jaiswal, Bharat Raj
Gupta, B. R.
|Applied and Computational Mechanics. 2014, vol. 8, no. 2, p. 157-176.
|University of West Bohemia
|Reiner-Rivlinova kapalina;Gegenbauerova funkce;proudová funkce;sféroid;tažná síla;faktor korekce stěny;sférický kontejner
|Keywords in different language:
|Reiner-Rivlin fluid;Gegenbauer function;stream functions;spheroid;drag force;wall correction factor;spherical container
|An analysis is carried out to study the flow characteristics of creeping motion of an inner non-Newtonian Reiner-Rivlin liquid spheroid r = 1+ ∑k=2∞αkGk(cos θ), here αk is very small shape factor and Gk is Gegenbauer function of first kind of order k, at the instant it passes the centre of a rigid spherical container filled with a Newtonian fluid. The shape of the liquid spheroid is assumed to depart a bit at its surface from the shape a sphere. The analytical expression for stream function solution for the flow in spherical container is obtained by using Stokes equation. While for the flow inside the Reiner-Rivlin liquid spheroid, the expression for stream function is obtained by expressing it in a power series of S, characterizing the cross-viscosity of Reiner-Rivlin fluid. Both the flow fields are then determined explicitly by matching the boundary conditions at the interface of Newtonian fluid and non-Newtonian fluid and also the condition of impenetrability and no-slip on the outer surface to the first order in the small parameter ε, characterizing the deformation of the liquid sphere. As an application, we consider an oblate liquid spheroid r = 1+2εG2(cos θ) and the drag and wall effects on the body are evaluated. Their variations with regard to separation parameter, viscosity ratio λ, cross-viscosity, i.e., S and deformation parameter are studied and demonstrated graphically. Several well-noted cases of interest are derived from the present analysis. Attempts are made to compare between Newtonian and Reiner-Rivlin fluids which yield that the cross-viscosity μc is to decrease the wall effects K and to increase the drag DN when deformation is comparatively small. It is observed that drag not only varies with λ, but as η increases, the rate of change in behavior of drag force increases also.
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|Volume 8, number 2 (2014)
Volume 8, number 2 (2014)
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