The motion induced between radially extensional plates with one or both plates shrinking

• Flow between shrinking plates is studied.
• Solutions depend on a Reynolds number R and the stretching ratio σ.
• Small-R solutions and large-R asymptotics are found.
• No bifurcations or dual solutions are found.

Flow between the radial extensional motion of parallel plates is studied for two cases. In the first case one plate stretches at rate a while the other plate shrinks at rate b   and in the second case both plates shrink. Both cases can be considered by defining stretching ratio as σ=b/|a|σ=b/|a|. When both plates shrink one can find solutions in the region σ<−1σ<−1 from those found in the region −1≤σ≤0−1≤σ≤0. This feature is not available when one plate stretches and the other shrinks and thus σ   must be varied over the region σ≤0σ≤0 to cover all possible solutions. Solutions are also dependent on a Reynolds number R=|a|h2/νR=|a|h2/ν where h is the plate separation distance and ν is the kinematic viscosity of the fluid. For both problems studied, we have determined the R=0 solutions and their large-R   asymptotic behaviors. Using two numerical techniques, no bifurcated solutions were encountered. Results are presented in graphical form for the radial pressure gradient, lower and upper wall shear stresses, and velocity profiles for these axisymmetric flows. A region of zero wall shear stress exists for stretching/shrinking plates whilst the wall shear stresses for shrinking/shrinking plates are never zero. An interesting singular limit in solution behavior as R→∞R→∞ is found for the shrinking/shrinking plate flow.