Viscous fingering in polymer solutions

Characteristics of viscous fingering are investigated by pushing air in a radial Hele-Shaw cell, where hydroxypropyl methyl cellulose (HPMC) solutions are placed, as a function of temperature. High molecular weight HPMC sample was used since its solution leads to a strong shear thinning due to chain entanglements. The resulting patterns show a systematic change from side branching to skewering patterns through the tip-splitting patterns with an increase in the injection pressure, irrespective of temperature. The characteristic quantities of the pattern growth, such as finger velocity and finger width, are evaluated. Darcy's law modified by taking into account the effective viscosity at a shear rate imposed to HPMC solutions is compared with the measured finger velocity, and good agreement is obtained. The finger width shows a broad maximum where the tip-splitting patterns are observed.