The unsteady motion of a sphere in an elastico-viscous liquid
Consideration is given to the unsteady motion of a sphere moving under a constant force in elastico-viscous liquid, the sphere being initially at rest. The problem is solved by the familiarLaplace-transform method. It is shown that the presence of elasticity in the liquid increases the velocity of the sphere. This increase is very pronounced for small values of the time, but is not very significant for large values of the time. It is concluded that the time taken to reach the “terminal” velocity is unaffected by the presence of elasticity in the liquid.
Formulae are given which may be of use to experimentalists who use the “falling-ball” method to determine the zero shear-rate viscosity.
KeywordsPolymer Viscosity Constant Force Unsteady Motion
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