title: Effect of confinement on the deformation of microfluidic drops.
abstract: We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents 2.59±0.28 and 0.91±0.05, respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a nondimensional parameter Caδ2, where Ca is the capillary number (proportional to the strain rate and the drop size) and δ is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.
authors.affiliation: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
authors.forename: Camilo
authors.initials: C
authors.lastname: Ulloa
authors.affiliation: Université Paris-Est Marne-La-Vallée, 5 boulevard Descartes, 77545 Marne-La-Vallée Cedex 5, France.
authors.forename: Alberto
authors.initials: A
authors.lastname: Ahumada
authors.affiliation: Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
authors.forename: María Luisa
authors.initials: ML
authors.lastname: Cordero