Two flat, rectangular plates with lateral dimension w X1 lie parallel, one above the other, a...

  

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Two flat, rectangular plates with lateral dimension w X1 lie parallel, one above the other, a distance h apart. The gap between them is filled with molten polymer. One plate is fixed; the other moves parallel to it in the direction of dimension I at velocity v, causing the fluid to be sheared. (1) Show that the fluid is displaced past the stationary plate with volume flow rate Q given by vhw Q = %3D (2) Find the equal and opposite shear forces which must be applied to the plates in order to sustain the deformation, assuming the polymer to be: (i) Newtonian with viscosity µ; and (ii) non-Newtonian, obeying the power law (eqn 7.18) with apparent viscosity uo at shear stress To, and with power-law exponent n. Two flat, rectangular plates with lateral dimension w X1 lie parallel, one above the other, a distance h apart. The gap between them is filled with molten polymer. One plate is fixed; the other moves parallel to it in the direction of dimension I at velocity v, causing the fluid to be sheared. (1) Show that the fluid is displaced past the stationary plate with volume flow rate Q given by vhw Q = %3D (2) Find the equal and opposite shear forces which must be applied to the plates in order to sustain the deformation, assuming the polymer to be: (i) Newtonian with viscosity µ; and (ii) non-Newtonian, obeying the power law (eqn 7.18) with apparent viscosity uo at shear stress To, and with power-law exponent n.