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On edge effects in rheometry

Consideration is given to the influence of edge effects on rheological measurements. To facilitate this, we discuss theoretically the flow generated by the slow steady rotation of a solid of revolution in an elastico-viscous liquid confined by convenient bath surfaces. The relevant linear partial differential equations are solved numerically. The simple problem of a rotating sphere and a concentric spherical container, for which an exact analytic solution is available, is first discussed to justify the method employed, and to indicate the necessary conditions to obtain a given accuracy. The numerical method is then applied to the case of a cone of finite dimensions rotating in a bath of elastico-viscous liquid. The predicted flow is shown to be in good agreement with experimental observations. Application of the theory to rheogoniometric situations indicates that edge effects are not likely to be as significant as has been conjectured in the past.