Instabilities in a bare Hele-Shaw cell at high Viscosity Ratios

Master's thesis by Jule Thome, August 2017

In my master's thesis, I developed an experimental setup to observe fingering patterns as a result of viscous instabilities in a quasi two-dimensional flow field.

Why is this interesting?

Viscous instabilities occur whenever a less viscous fluid displaces a more viscous one. This is a setup that can play a role in many natural and technical systems. Some examples are oil recovery, carbon dioxide sequestration, or groundwater flow with a contaminant that changes its viscosity.

Another angle is, that the data gained from a physically well-understood experiment such as mine can be used to build bridges to numerical simulation. There are multiple things that can be learned by comparing experiments to numerical simulation. Sometimes this can help to understand and explain the observed phenomena. Often, simulations do not incorporate the full physical system, as they might be truly one or two-dimensional where the experiment is not, or some processes might be neglected. The comparison to experiments can then show what effect these non-represented processes have on the system. The underlying goal is to find generally applicable methods how experimental data and numerical simulations can be combined to get a more complete picture of the system.

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The Setup

To create viscous instabilities, I displaced glycerol-mixture (highly viscous) by dyed water (less viscous) in a Hele-Shaw cell. A Hele-Shaw cell are two plane parallel glass plates, held at a very small distance, the gap width d. In my case, the gap width was of the order of around 1mm to 2mm, while the glass plates have an area of 500mm by 300mm. Important to note is, that the plates are never perfectly parallel. Due to the technical setup of how the plates are held in place, d is in general larger at the center of the flow domain.

A diffusive light source illuminates the cell from behind while the experiment is observed by a CCD camera. All of these components are mounted on an axis that can be tilted, such that the flow direction inside the cell is horizontal. Thus, there is no gravitational force acting in flow direction.

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I was able to show that it is possible to observe viscous instabilities over a range of varying forcing strengths and viscosity ratios (viscosity of the used glycerol-mixture divided by that of water).

On the right, you can get an impression how typical fingering patterns look and develop over time. Water (appearing blue) is pumped into the cell and displaces the more viscous glycerol-mixture (yellow).

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