Rheology of foams. I. Theory for dry foams
A two-dimensional model for foams having gas volume fraction approaching unity has been developed. A general expression for the stress tensor is obtained which gives the total stress in terms of the shape of the cells, interfacial tension, the initial cell orientation, and the rate of deformation in the liquid. A formalism for describing cell deformation is also presented. By assuming hexagonal, monodisperse foam cells, we are able to obtain analytical expressions for stresses for small shearing and elongational deformations (below the yield strain) as well as for steady shear flow. For strains below the yield point, the stress-strain relation is independent of initial cell orientation. However, the critical strain varies with orientation, and therefore, the yield stress, \(\tau_ 0\), is a function of orientation.
scientific article; zbMATH DE number 4005811