Modeling drop deformations and rheology of dilute to dense emulsions

We highlight the current state-of-the-art in modeling emulsion rheology, ranging from dilute to jammed dense systems. We focus on analytical and numerical methods developed for calculating, computing, and tracking drop deformation in response to viscometric flows and deriving constitutive models for flowing emulsions. We identify material properties and dimensionless parameters, collate and catalog the small deformation theories and resulting expressions for viscometric quantities, and take stock of challenges for capturing connections between drop deformation, morphology, and rheology of emulsions. We highlight the substantial progress in providing quantitative descriptions of the rheological response using analytical theories, scaling, and computational fluid dynamics. We illustrate how macroscopic rheological properties emerge from microscopic features including the deformation and dynamics of noninteracting or interacting drops, and molecular aspects that control the interfacial properties.