Capillary Rise of a Non-Newtonian Power Law Liquid: Impact of the Fluid Rheology and Dynamic Contact Angle

Abstract

The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.

The fastest capillary penetration of power-law fluids

“…First, we compare the model for the capillary-driven power-law fluids in a single tube with experimental results (Digilov, 2008) in Fig. 2.…”

“…The capillary dynamics of the power-law fluids in a uniform circular tube was expressed as a function of n, and the flow was found to be retarded when the liquid became more strongly shear-thinning with n o1 (Turian and Murad, 2005). The impact of fluid rheology and dynamic contact angle on the capillary rise of power-law fluid was explored experimentally and theoretically (Digilov, 2008). The shearthinning fluid under gravity begins to rise faster than the shear thickening counterpart, but they have the same equilibrium height with the Newtonian liquid due to self-retardation (Digilov, 2008).…”

“…The impact of fluid rheology and dynamic contact angle on the capillary rise of power-law fluid was explored experimentally and theoretically (Digilov, 2008). The shearthinning fluid under gravity begins to rise faster than the shear thickening counterpart, but they have the same equilibrium height with the Newtonian liquid due to self-retardation (Digilov, 2008). For power-law fluids in conical tubes, asymmetric flow times have been found from different ends of the tubes, and the asymmetry is strengthened by shear-thinning fluid but weakened by the shearthickening fluid (Berli and Urteaga, 2014).…”

Influence of Surfactant Concentration in the Emulsions on the Process of Oleophilic/Hydrophobic Porous Medium Imbibition

“…mass/height change) and time [1], [5]- [10]; study of the dependence between the characteristics of porous structure and the imbibition rate [1], [8]- [10]; and study of the effect of penetrating liquid characteristics on this process [5]- [7]. Majority of the presented results has been related to the imbibition with single-phase liquids [1]- [3], [5]- [11], while the issues concerning multiphase liquids, viz.…”

Analysis of emulsions concentration changes during imbibition in porous sorbents

“…Moreover, the various models mainly based on fundamental equations such as Lucas-Washburn, Hagen-Poiseuille, and LaplaceYoung were proposed to approximate the experimental data concerning single-phase liquids imbibition in the capillaries and different porous media. Many of such models consider the influence of dynamic contact angle on the capillary rise (Zhmud et al 2000;Hamraoui and Nylander 2002;Digilov 2008;Hilpert 2010). Another type related to the spontaneous imbibition of a wetting permeant into gas-saturated porous media consisting of a complex structure of pores and based on fractal geometry (Benavente et al 2002;Zhao and Li 2009;Cai et al 2010Cai et al , 2011Cai et al , 2012.…”