Liquid Flow through a ruptured seal

[tejasinamdar]

I am researching flow through blister packs and trying to derive an equation that can relate flow rate to a plunger position.
If I cannot describe the problem well, I will upload a picture that can give a better idea.

I have an igloo shaped blister pack made of aluminum foil. A plunger moves downward into the dome shape of the igloo. The blister pack is filled with liquid which is released once a seal at the center of the igloo entrance is broken. The increase in pressure inside the deformed blister pack causes the break in the seal.

I want to find out the flow just at the instant the seal breaks as well as how the flow rate changes as time passes/plunger moves inwards.

Some of the challenges I am facing are -
The plunger impresses into the dome for a finite distance until the seal is finally broken. Since the liquid (water) is incompressible, it implies that the foil expands slightly to accommodate this loss of volume. The expansion of the foil has it's own elasticity and will store pressure/energy until the seal is broken. This stored energy will contribute to the pressure from the plunger when the seal breaks.

There is a very high possibility that I may be complicated things for no good reason. Please tell me if I could model it simpler.
In summary, I want to find the flow rate against the position of the plunger into the dome.

Any help towards approaching the problem will be highly appreciated.

Thank You !

 

[AndyW]

Dear researcher,

Thank you for sharing your research topic with us. The problem you are trying to solve is very interesting and has practical applications in the pharmaceutical industry. As you have rightly pointed out, the flow through blister packs can be affected by various factors such as the plunger position, foil expansion, and stored energy.

To derive an equation that relates flow rate to plunger position, you will need to consider the following factors:

1. Geometry of the blister pack: The shape and size of the blister pack will have an impact on the flow rate. A larger blister pack with a larger dome will have a higher flow rate compared to a smaller one.

2. Plunger position: As the plunger moves into the dome, it applies pressure on the liquid, causing it to flow out of the blister pack. The flow rate will increase as the plunger moves deeper into the dome.

3. Foil expansion: The expansion of the foil will also affect the flow rate. As the plunger moves deeper into the dome, the foil will expand, creating more space for the liquid to flow out.

4. Elasticity of the foil: The elasticity of the foil will also play a role in the flow rate. As the plunger applies pressure, the foil will stretch and store energy, which will contribute to the flow rate when the seal is broken.

To model this problem, you could use the principles of fluid mechanics and consider the Bernoulli's equation, which relates pressure, velocity, and elevation in a fluid flow. You could also use the continuity equation, which states that the mass flow rate remains constant in a closed system.

In addition, you could also conduct experiments to validate your equation and observe how the flow rate changes with different factors such as plunger position, blister pack size, and foil elasticity.

I hope this helps you in approaching the problem. Good luck with your research!