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

Abstract

We present the dynamic velocity profiles of a Newtonian fluid ͑glycerol͒ and a viscoelastic Maxwell fluid ͑CPyCl-NaSal in water͒ driven by an oscillating pressure gradient in a vertical cylindrical pipe. The frequency range explored has been chosen to include the first three resonance peaks of the dynamic permeability of the viscoelastic-fluid-pipe system. Three different optical measurement techniques have been employed. Laser Doppler anemometry has been used to measure the magnitude of the velocity at the center of the liquid column. Particle image velocimetry and optical deflectometry are used to determine the velocity profiles at the bulk of the liquid column and at the liquid-air interface respectively. The velocity measurements in the bulk are in good agreement with the theoretical predictions of a linear theory. The results, however, show dramatic differences in the dynamic behavior of Newtonian and viscoelastic fluids, and demonstrate the importance of resonance phenomena in viscoelastic fluid flows, biofluids in particular, in confined geometries.

Non-Steady Wall-Bounded Flows of Viscoelastic Fluids Under Periodic Forcing

“…In particular, we present a detailed theoretical derivation of the velocity field and the dynamic permeability in flows at small both Reynolds and Weissenberg numbers. As we shall see, our finding suggests that the (additional) Newtonian component of stresses due to solvent viscosity might leads to the damping of the local dynamic response as the forcing frequency increases, a fact observed in ( [4], [5]). We also investigate the behavior of these quantities in weakly compressible flows.…”

“…The former source is vanishingly small, since the Reynolds number is set R e 10 −4 (see [4]). As for the elastic sources of nonlinearity we must also say that, in [5], measurements were carried out at a more detailed level, namely, the whole velocity field was explored along the cross-section and at different heights from the moving piston. The former measurements confirm the hypothesis (to a certain extent) that the velocity field depends only on the radial coordinate.…”

“…Now, following the same procedure as in Refs. ( [3], [4], [5]) we shall calculate the average velocity over a cross section. Thus,…”

“…( [4], [5]), by means of velocity measurements at the center of a viscoelastic fluid column (N ayCl/N aSal in water ) flowing inside a straight pipe of circular cross section [4] and more recently in the entire cross section of the fluid column [5], it was found a dramatic enhancement in the dynamic response to an oscillating periodic pressure gradient, that is, the fluid response, measured in terms of the velocity for a given amplitude of the pressure gradient, exceeds by several orders in magnitude that obtained for the steady case. It is noteworthy that most of the features observed in experiments, namely, the values of the driving frequencies at which the resonant behavior takes place and the formation of Couette-like flows as the driving frequency increases are successfully reproduced by a linear Navier-Stokes and Maxwell constitutive equations ( [3], [5], [6]). Nevertheless, theoretical predictions within this model overestimate the magnitude of the response amplitude as well as the root mean square velocity at the pipe axis and the velocity at certain points of the cross section of the fluid column.…”

Hydrodynamics of a Confined Meniscus in a Square Capillary Tube at Low Capillary Numbers

“…Till now, a variety of experimental and numerical techniques have been adopted to analyze the flow field inside microchannels (Torralba et al, 2005). One popular contemporary technique is the micro-Particle Image Velocimetry (µ-PIV), which offers a powerful, nearly nonintrusive tool to study the liquid flow field.…”