Enhancement in the dynamic response of a viscoelastic fluid flowing through a longitudinally vibrating tube

Abstract

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated: (A) the dynamic permeability and (B) the function F (κ) that measures the deviation from Poiseuille flow friction as a function of frequency parameter κ. This provides a more complete theory of flow of Maxwell fluid through the longitudinally oscillating cylindrical tube with the oscillating pressure gradient, which has important practical applications. This study has clearly shown transition from dissipative to elastic regime in which sharp enhancements (resonances) of the flow are found.

Experimental observation of dramatic differences in the dynamic response of Newtonian and Maxwellian fluids

“…The use of the dynamic permeability as originally proposed [1] however, is not quite correct for some of these systems since the fluid does not behave as a Newtonian fluid but shows viscoelastic features. Theoretical analyzes of viscoelastic fluids have recently predicted an interesting enhancement in the dynamic permeability of several orders of magnitude in comparison with the static permeability [10,11,12,13]. This behavior is due to the coupling between the elastic behavior of the fluid and the geometry of the container and is completely different from the pure dissipative behavior of Newtonian fluids.…”

“…An increase in the flow rate of a viscoelastic fluid flowing in a tube under oscillating conditions was discovered several years ago [14,15,16,17] but up to now, the experimental measurements in terms of a frequency-dependent response had not been performed. Some theoretical studies have explored interesting consequences of the enhancement of the dynamic permeability in different systems including viscoelastic fluids [12,13,18,19,20,21,22,23]. The variety of systems where an oscillating pressure gradient can be imposed to a viscoelastic fluid is wide, for instance, from the oil recovery problem [24] to the dynamic analysis of fluid transport in animals (including the human body [25]).…”

On the high frequency oscillatory tube flow of healthy human blood

“…The frequency ω r (say) where the maximum occurs may be viewed as a resonant frequency. The phenomena of resonant frequencies and flow enhancement in oscillatory pipe flow is well known in both the experimental and theoretical viscoelastic literature and further discussion of these may be found, for example, in [2,8,13,32,41,46]. A helpful review of earlier work is to be found in the article of Siginer [35].…”

Viscoelastic Effects on the Entropy Production in Oscillatory Flow between Parallel Plates with Convective Cooling

“…In a similar way, the effective thermal diffusivity of a Newtonian fluid in a duct subjected to a zero-mean oscillatory flow may reach a maximum for a specific oscillation frequency and lead to heat transfer enhancement [4,5]. Moreover, in the case of a viscoelastic fluid flowing in a tube, the dynamic permeability may be enhanced at given resonant oscillation frequencies [6,7,[9][10][11]. Recently, attention has been directed to oscillatory flows at high frequencies under conditions where inertial effects are negligible with the aim at using them in microfluidics applications [12].…”