HandsOn 16 - The Hele-Shaw Experiment with Carrageenan

I. Introduction

II. Preparing Carrageenan

III. Observational Analysis

III. Observational Analysis

The reason that fluids flow is because of pressure differences across the fluid. For example, when you suck on a straw the fluid flows up the straw because atmospheric pressure at the bottom of the straw is greater than the pressure in your mouth. Similarly, when you apply pressure with the syringe at the central opening of the Hele-Shaw plates, fluid flows into the cell because the pressure at the center is greater than the atmospheric pressure surrounding the open edges of the cell.

To understand what follows it is useful to know that usually the speed of fluid flow in a pipe, or between two plates, is proportional to the pressure difference across the fluid, and inversely proportional to the distance over which that pressure difference is maintained. For example, if you suck harder on a straw, further reducing the pressure in your mouth, this increases the pressure difference across the straw (since atmospheric pressure remains constant), and the fluid flows faster. Similarly, if you use a shorter straw, the same pressure difference exists across a shorter length and the fluid flows faster. In the case of the Hele-Shaw cell, if your plates are smaller in diameter, then for the same applied pressure on the syringe, the fluid between the plates will flow faster.

Q4.24: Do you see an analogy between the applied pressure in the Hele-Shaw experiment and the applied voltage in the electrochemical deposition experiment?

For a given applied pressure difference, the speed of fluid flow between the plates of the Hele-Shaw cell is proportional to the square of the spacing between the plates. Thus, if you double the spacing between the plates, you quadruple the flow rate if all other conditions are kept constant.

1. When you inject the glycerol or carrageenan into the air-filled cell, watch the interface for bumps. When a more viscous fluid invades a less viscous one (e.g., the glycerol or carrageenan invading air), the interface is "stable'' in the sense that any bumps which form die away. The interface "heals'' and returns to being smooth and symmetric. If you videotaped your experiment, or recorded it into a computer, play it back and watch this phenomenon again. Alternatively, repeat the experiment if you did not observe this phenomenon the first time.


2. By contrast, when you inject the water into the glycerol, or the acid into the carrageenan, the interface does not remain symmetric but breaks up into viscous fingers, the name given to the mitten-like protrusions that result when bumps on an interface grow. We say that the interface is "unstable'' when a less viscous fluid is injected into a more viscous one.

                        

Q4.25: Repeat the experiment, or study your video or pictures of it, and try to determine when the bumps start growing. Is there an initial symmetric interface at the outset? Or do viscous fingers originate directly beneath the nozzle?

Q4.26: Either by repeating the experiment or referring to your film, study the growth of individual fingers as they advance. Does a finger retain its shape and grow like an inflated long narrow balloon? Or do fingers break up and form multiple new fingers? Do all fingers grow, or do some stop advancing and become static? Where are the ones located that become static? Where do advancing fingers split?

The growth of the branching tree structure of viscous fingers is a primary example of how branching structures develop. A bump appears at the interface. The bump grows faster than adjacent areas of the interface and develops into a finger. The finger itself then splits and forms multiple branches growing from new bumps.

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