Radially Interrupted Viscous Fingers in a Lifting Hele-Shaw Cell

TL;DR

This study investigates how concentric grooves in a lifting Hele-Shaw cell accelerate viscous fingering by causing fingers to reform and gain speed at each groove, significantly speeding up the process.

Contribution

It introduces the effect of circular grooves on viscous finger dynamics in a lifting Hele-Shaw cell, demonstrating how grooves accelerate finger progression.

Findings

Grooves cause fingers to reform and speed up at each encounter.

Fingers reach the center faster in grooved cells compared to normal cells.

Velocity of fingers varies with time and groove interaction.

Abstract

Viscous fingers have been produced in the lifting Hele-Shaw cell, with concentric circular grooves etched onto the lower plate. The invading fluid (air) enters the defending newtonian fluid - olive oil as fingers proceeding radially inwards towards the centre. The fingers are interrupted at the circular groove, and reform as secondary fingers. The effect of the grooves is to speed up the fingering process considerably and the fingers now reach the centre much faster. We explain this by comparing the variation in velocity of the fingers in the normal HS cell and the grooved cells with time. In the normal HS cell the fingers move fastest on initial formation and slow down later. Since in case of the grooved plate, the fingers reform and receive a boost in their speed each time they encounter a groove, the fingers proceed to the centre faster. PACS nos. 47.20.Gv, 47.54.+r, 68.03.-g