Slow Plastic Flow of a Bingham Material Between Rotating Concentric Infinite Cylinders with Axial Roughness

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In this paper slow plastic flow of a Bingham solid between rotating concentric infinite cylinders with axial roughness is investigated. The effects of cylinder perturbation on the velocity distribution are determined. Sinusoidal roughness given by εN_1(z)=h_1 sin(2πz/λ_1) and εN_2(z)=h_2 sin(2πz/λ_2), where ε is the small parameter of the boundary perturbation, is considered as an illustration. Two special cases of practical importance are studied. In the first, the roughness wave-lengths are large as compared to the radii of the cylinders and in the second, spacing between the cylinders is taken small. The average moment per unit length on the cylinders is calculated and the order of perturbation in the moment is dermined. By taking h_1=h_2=10^<-3>cm, b-a=10^<-2>cm and a=1cm, the moment M_2 on the outer cylinder has been calculated and compared with the moment M_0, when the cylinders are taken smooth. For Bingham number equal to 0,1,2 the ratio (M_2-M_0)/M_0 is determined for various values of λ_2/λ_1, the ratio of wavelengths. It is found that, with the increase of Bingham number, the value (M_2-M_0)M_0 increases for λ_2/λ_1<1 for the considered cases.
社団法人応用物理学会の論文
1971-11-05