Controlling viscoelastic flow in microchannels with slip.

We show that viscoelastic flow in a microchannel under a dynamic pressure gradient dramatically changes with the value of the apparent slip. We demonstrate this by using classical hydrodynamics and the Navier boundary condition for the apparent slip. At certain driving frequencies, the flow is orders of magnitude different for systems with and without slip, implying that controlling the degree of hydrophobicity of a microchannel can lead to the control of the magnitude of the flow. We verify this for viscoelastic fluids with very different constitutive equations. Moreover, we demonstrate that flow, given a value of the apparent slip, is a non-monotonic function of the driving frequency and can be increased or reduced by orders of magnitude by slightly changing the frequency of the driving pressure gradient. Finally, we show that, for dynamic situations, slip causes and effectively thicker channel whose effective thickness depends on frequency. We have calculated relevant quantities for blood and a polymeric fluid in order to motivate experimental studies.

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.

Dynamic characterization of permeabilities and flows in microchannels.

We make an analytical study of the nonsteady flow of Newtonian fluids in microchannels. We consider the slip boundary condition at the solid walls with Navier hypothesis and calculate the dynamic permeability, which gives the system's response to dynamic pressure gradients. We find a scaling relation in the absence of slip that is broken in its presence. We discuss how this might be useful to experimentally determine--by means of microparticle image velocimetry technology--whether slip exists or not in a system, the value of the slip length, and the validity of Navier hypothesis in dynamic situations.

Experiments of periodic forcing of Saffman-Taylor fingers.

We report on an experimental study of long normal Saffman-Taylor fingers subject to periodic forcing. The sides of the finger develop a low amplitude, long wavelength instability. We discuss the finger response in stationary and nonstationary situations, as well as the dynamics towards the stationary states. The response frequency of the instability increases with forcing frequency at low forcing frequencies, while, remarkably, it becomes independent of forcing frequency at large forcing frequencies. This implies a process of wavelength selection. These observations are in good agreement with previous numerical results reported in [Ledesma-Aguilar, Phys. Rev. E 71, 016312 (2005)]. We also study the average value of the finger width, and its fluctuations, as a function of forcing frequency. The average finger width is always smaller than the width of the steady-state finger. Fluctuations have a nonmonotonic behavior with a maximum at a particular frequency.

Controlling viscoelastic flow by tuning frequency during occlusions.

We study the flow of a viscoelastic fluid flowing in an occluded tube due to either central or peripheral obstructions. We show that, by driving the fluid with a dynamic pressure gradient at the frequency that maximizes the dynamic permeability of the obstructed system, the magnitude of the flow can partially be recovered without the removal of the obstruction. We compare the results obtained for the two types of occlusions studied and find that flow recovering is larger in the case of central occlusions.

Phase field approach to spatial perturbations in normal Saffman-Taylor fingers.

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.