Stability of a Non-Newtonian Liquid Film Flowing Down an Inclined Plane

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Abstract
A layer of a non‐Newtonian liquid, of which the constitutive equation is triply nonlinear, flows down an inclined plane under the action of gravity. The stability of the flow against wave formation is investigated. With M denoting a parameter involving the first and the second viscosities, the critical Reynolds number is given as a function of M and the slope of the plane, for small values of M. The theory presented here shows how free‐surface instability of non‐Newtonian fluids can be attacked, and provides a basis for stability experiments with non‐Newtonian fluids.

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