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• W2039929514 abstract "The steady flow is considered of a Newtonian fluid, of viscosity μ, between contra-rotating cylinders with peripheral speeds U 1 and U 2 . The two-dimensional velocity field is determined correct to O ( H 0 /2 R ) 1/2 , where 2 H 0 is the minimum separation of the cylinders and R an ‘averaged’ cylinder radius. For flooded/moderately starved inlets there are two stagnation–saddle points, located symmetrically about the nip, and separated by quasi-unidirectional flow. These stagnation–saddle points are shown to divide the gap in the ratio U 1 [ratio ] U 2 and arise at [mid ] X [mid ]= A where the semi-gap thickness is H ( A ) and the streamwise pressure gradient is given by dP / dX =μ( U 1 + U 2 )/ H 2 ( A ). Several additional results then follow. (i) The effect of non-dimensional flow rate, λ: A 2 =2 RH 0 (3λ−1) and so the stagnation–saddle points are absent for λ<1/3, coincident for λ=1/3 and separated for λ>1/3. (ii) The effect of speed ratio, S = U 1 / U 2 : stagnation–saddle points are located on the boundary of recirculating flow and are coincident with its leading edge only for symmetric flows ( S =1). The effect of unequal cylinder speeds is to introduce a displacement that increases to a maximum of O ( RH 0 ) 1/2 as S →0. Five distinct flow patterns are identified between the nip and the downstream meniscus. Three are asymmetric flows with a transfer jet conveying fluid across the recirculation region and arising due to unequal cylinder speeds, unequal cylinder radii, gravity or a combination of these. Two others exhibit no transfer jet and correspond to symmetric ( S =1) or asymmetric ( S ≠1) flow with two asymmetric effects in balance. Film splitting at the downstream stagnation–saddle point produces uniform films, attached to the cylinders, of thickness H 1 and H 2 , where formula here provided the flux in the transfer jet is assumed to be negligible. (iii) The effect of capillary number, Ca : as Ca is increased the downstream meniscus advances towards the nip and the stagnation–saddle point either attaches itself to the meniscus or disappears via a saddle–node annihilation according to the flow topology. Theoretical predictions are supported by experimental data and finite element computations." @default.
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• W2039929514 date "1998-09-10" @default.
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• W2039929514 title "Stagnation–saddle points and flow patterns in Stokes flow between contra-rotating cylinders" @default.
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• W2039929514 doi "https://doi.org/10.1017/s0022112098002031" @default.
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