Measurements of the bulk and interfacial velocity profiles in oscillating Newtonian and Maxwellian fluids

Pulsatile parallel flow of air and a viscoelastic fluid with multiple characteristic times. An application to mucus in the trachea and the frequency of cough

We study the dynamics of a binary fluid, where the two fluids are flowing parallel to each other in a cylindrical geometry, and driven by a pulsatile pressure gradient. One of the fluids is a low viscosity Newtonian fluid, the other one is viscoelastic. In order to be able to apply the model to different biofluids, we consider that the viscoelastic fluid has several characteristic times. We characterize the dynamics of the fluids as generalized Darcy's laws, with linear response functions to pulsatile pressure gradients, whose parameters are coupled for both fluids through the fluid-fluid boundary conditions. We apply our results to the dynamics of mucus and air in the trachea and find that the frequency that allows for a larger movement of the mucus, coincides with the experimental frequency of cough. This allows us to propose a plausible explanation for the frequency of cough in healthy individuals, a mechanical process to expel noxious substances from the respiratory system.

Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. The model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.

Stokes layers in oscillatory flows of viscoelastic fluids

Oscillatory flows of viscoelastic fluids are studied from the perspective of Stokes viscoelastic layers. We identify the governing dimensionless variables, and study the flows in a general way for fluids with linear rheology. Nonlinearities can be treated perturbatively to account for reported flow instabilities. This article is part of the theme issue 'Stokes at 200 (Part 1)'.

Frequency-induced stratification in viscoelastic microfluidics

We present a mechanism in the field of microfluidics by which the stratification of a viscoelastic fluid can be induced in a channel on the microscale by applying a dynamic pressure gradient at frequencies within the range of sound. Stratification is obtained with identical layers, parallel to the channel walls, whose number can be tailored. These layers are separated by 2D zero-velocity planes. This would allow different tracer particles with small diffusion coefficients to be confined in different fluid layers within the same microchannel. We obtain analytical results that allow us to make theoretical predictions regarding the possible experimental realization of stratification in a microchannel using a biofluid. We find a relation among the diffusion coefficient, fluid properties, and microchannel thickness that establishes a condition for the confinement of tracer particles to a layer. This mechanism has potential use in micrototal analysis systems and MEMS-containing viscoelastic fluids.

Instabilities in the oscillatory flow of a complex fluid

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11.5 Hz. The Newtonian fluid exhibits a laminar flow regime, independent of the axial position, in the whole range of drivings. For the complex fluid, instead, the parallel shear flow regime exhibited at low amplitudes [Torralba, Phys. Rev. E 72, 016308 (2005)] becomes unstable at higher drivings against the formation of symmetric vortices, equally spaced along the tube. At even higher drivings the vortex structure itself becomes unstable, and complex nonsymmetric structures develop. Given that inertial effects remain negligible even at the hardest drivings (Re < 10(-1)), it is the complex rheology of the fluid that is responsible for the instabilities observed. The system studied represents an interesting example of the development of shear-induced instabilities in nonlinear complex fluids in purely parallel shear flow.