Singular behavior of microfluidic pulsatile flow due to dynamic curving of air-fluid interfaces

Experimental Resonances in Viscoelastic Microfluidics

“…It therefore cannot be used to model fronts in imbibition-like systems, where the pressure drop has always the same sign and the interface curvature is due to wetting. In our case, curvature effects due to wetting cancel out since they have opposite signs on the left and right side interfaces [33], and the dynamics of the slug will be governed by the instantaneous interfacial curvatures caused by pulsatile forcing.…”

“…A stress tensor of the form (3) for a material consisting of a volume of fluid and two air-fluid interfaces, has not been introduced in the literature, to the best of our knowledge, since classical treatments describe both fluid phases and apply boundary conditions at air-fluid interfaces, rather than describing the system fluid-interfaces as a composite material. Vazquez-Vergara et al [33] together with discussion in the previous paragraph, show that introduction of a slug stress tensor, as the one in Equation ( 3), is a consistent approach to describe the zero-mean flow, linear pulsatile dynamics of Newtonian slugs.…”

“…Because of this, we present a model for the uniaxial dynamics of a viscoelastic slug, taking into account the presence of interfaces and the viscoelastic character of a single-relaxation-time fluid, that could be extended to models containing more characteristic times. We build up a model for the dynamics of viscoelastic slugs over a model presented for the dynamics of a Newtonian slug [33].…”

“…This model has given a correct description of the experimental dynamics of a water slug and of a 70% glycerol solution in water slug, when interfacial curvatures are considered to be a response to a dynamic external pressure gradient p driving /L. Details of the derivation of Equation ( 2) can be seen in [33].…”

“…Recently, a model to study the dynamics of a pulsatile (zeromean flow) fluid slug, consisting of a Newtonian fluid and two air-fluid interfaces, driven by a periodic pressure gradient in a rectangular microchannel, has been proposed [33]. In that model, a stress tensor for a Newtonian fluid, together with Laplace condition for the pressure jump at both sides of the curved air-fluid interfaces, has been considered.…”