The Hele-Shaw Experiment with Glycerin

HandsOn 15 - The Hele-Shaw Experiment with Glycerin

The viscosity of fluids plays an important part in the Hele-Shaw experiment, supplied in the accompanying laboratory kit. Figure shows a Hele-Shaw cell with its two plates of plastic separated by cover slips (little squares of glass or plastic usually used to cover microscope slides). In each corner there are two cover slips, one on top of the other. Typically glass cover slips are between 130 and 160 micrometers in thickness. Plastic cover slips are roughly the same thickness. So the spacing between the plates is roughly 300 micrometers.

Figure 4.10: The Hele-Shaw cell. Fluid is injected through the center hole. The space between the plates is fixed by the thickness of two cover slips, one on top of the other placed in each corner of the cell.

In the experiment you will first inject glycerol through the central hole to fill the cell. After the cell is filled with glycerol, you will inject colored water as shown in Figure .

Figure 4.11: Hele-Shaw experiments showing the less viscous colored water injected into the more viscous glycerin.

Q4.20: Speculate: You will inject glycerol into the empty cell. As the glycerol spreads, what will be the shape of the boundary between glycerol and air? We call this boundary between two fluids the interface. Sketch the shape you predict for this interface, and provide a written argument to support your sketch. Was your prediction influenced by the viscosity difference between the glycerol and air? The symmetry of the cell? The narrowness of the cell spacing? The surface tension between the glycerol and air? Prior experience?

Q4.21: The cell is now filled with glycerol. With another syringe, inject water through the central opening. The water should have food coloring in it so that you can distinguish it from the glycerol and trace the interface between the water and glycerol. As the water advances, what will be the shape of the interface between the water and the glycerol? Sketch your predicted shape and write a brief argument supporting your sketch. Does your argument depend on the difference in viscosity between the water and glycerol? The symmetry of the cell? The narrowness of the cell spacing? The surface tension between the water and glycerol? Prior experience?

Using the apparatus supplied in your laboratory kit, you can now perform the experiments suggested above. For data collection it will be easiest to work with one or two partners and a copy of Table 4.2. If possible, use a video camera (or snap digital pictures) to record the experiment as it progresses.

Table 4.2: Data Table which should be used for both Hele-Shaw cell experiments.

DV V_T r

0.2 ml 0.2 ml

0.2 0.4

0.2 0.6

0.2 0.8

0.2 1.0

1. Assemble the cell as indicated in the instructions. Fill a syringe with approximately 20 cc of glycerol. Insert the syringe into the central opening, and slowly inject the glycerol. If you are patient, you can let the glycerol flow by itself into the cell. Otherwise, you can press the plunger of the syringe slowly downward.

As the glycerol enters the cell, study its interface carefully. (The interface is the boundary between the two fluids.) If bumps develop on the interface, watch what happens to them. By a bump we mean a deviation from a symmetrical, smooth interface. Does a small bump grow? Or does it recede with time and the interface "heal'' itself? What might give rise to the development of these bumps? What determines their lifetime?

2. The central opening on the plate should be filled with glycerol to the top in order to avoid introducing air bubbles. Fill the 1 cc syringe with water containing food color. Carefully attach the syringe to the nozzle. Inject roughly 0.2 cc of the water (at a rate of, say, 0.1 cc per second), watching the interface carefully. Measure and record the radius of the interface. If it is not symmetrical, approximate the average radius. Adding 0.2 cc at a time, repeat the measurement process until all the water has been injected.

3. Scan the interface with a flat bed scanner, or "grab'' the image of the interface using a digital camera connected to your computer.

Q4.22: As the glycerol approaches the edge of the cell what is the shape of the interface?

Figure 4.12: Plot your experimental measurements for the Hele-Shaw experiments on this graph. The two curves shown represent growing patterns of dimension 1 (the lower curve) and dimension 2 (the upper curve). Can you explain how these curves were drawn? Hint: The distance between plates is approximately 3 mm.

Q4.23: Plot your radius versus volume measurements on the graph shown in Figure 4.12. What can you say about the "dimension'' of the pattern you created?

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