Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2020-10, Vol.476 (2242), p.1-14
• Main Authors: Gorthi, Srinivas R., Meher, Sanjaya Kumar, Biswas, Gautam, Mondal, Pranab Kumar
• Format: Article
• Language: English
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2020.0496

We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald–de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling (Digilov 2008 Langmuir 24, 13 663–13 667 (doi:10.1021/la801807j)). Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation x ∼ √ t. Such a regime can be called the modified Washburn regime (Washburn 1921 Phys. Rev. 17, 273–283 (doi:10.1103/PhysRev.17.273)).