A back-of-the-envelope approach to boudinage mechanics

Abstract

Smith has shown from linear hydrodynamic stability that pinch-and-swell boudinage is possible only in a non-Newtonian material. By assuming uniaxial stress and strain and large viscosity contrast between the competent layer and the incompetent matrix, Smith's result can be derived in a very simple way. The one-dimensional force balance also predicts growth rates, although not dominant wavelengths. However, we question the ability of even linear stability analysis to accurately predict boudin widths.