Abstract
Many electrorheological fluids (ERFs) as fluids with microstructure demonstrate viscoplastic behaviours. Rheometric measurements indicate that some flows of these fluids may be modelled as the flows of a Herschel-Bulkley fluid. In this paper, the flow of a Herschel-Bulkley ER fluid—with a fractional power-law exponent—in a narrow clearance between two fixed surfaces of revolution with common axis of symmetry is considered. The flow is externally pressurized, and it is considered with inertia effect. In order to solve this problem, the boundary layer equations are used. The influence of inertia forces on the pressure distribution is examined by using the method of averaged inertia terms of the momentum equation. Numerical examples of externally pressurized ERFs flows in the clearance between parallel disks and concentric spherical surfaces are presented.
Highlights
Formulae and graphs presented here for the Herschel-Bulkley electrorheological fluids (ERFs) flows in the narrow clearance of constant thickness between parallel disks and concentric spherical surfaces shown in Figures 4 and 10 one may conclude that the pressure values (i) decrease with the increase of the modified Reynolds number Rλ, (ii) increase with the decrease of the nonlinearity index m, (iii) increase with the decrease of the de Saint-Venant ER number KSV, (iv) are larger between concentric spherical surfaces than these ones between parallel disks for 2m being natural numbers and large values of KSV, (v) for m being rational numbers it is inversely
For small values of the de Saint-Venant ER number KSV the influence of the Reynolds number Rλ on the pressure values is inconsiderable
For these values of KSV the Herschel-Bulkley ERF flows may be considered without inertia effects
Summary
The study of fluids with microstructures has gained much importance because of its numerous applications in various engineering disciplines such as chemical engineering, polymer processing, plastic forming foundry engineering, and engineering of lubrication [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. Several constitutive relations applied were used to model the non-Newtonian characteristics exhibited by some lubricants [7, 11, 13, 15, 16] Another ones of these phenomena are processes of vibration control and torque transmission. The electrorheological fluids (abbreviated to ERFs) have acquired a great relevance for supporting vibration control and torque transmission devices, based on the characteristic dependence of their viscosity on applied electric field strength. Since their initial discovery by Winslow [17], many particle-dispersion electrorheological fluids, consisting of dielectric particles dispersed in insulating oil, have been reported. To solve the problem we will use the lubrication approximation theory to the flow in a narrow clearance [8, 10, 15, 16, 25]
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