Fluid dynamics: half submerged straw opening

[rallyka2001]

Homework Statement

This is not a set question but a problem statement for an investigation.

I am trying to understand the physics behind drinking through a straw, but not when the straw is fully submerged in the drink but at the end of the drink when the liquid and air both pass up the straw and you get the slurping noise.

I understand that when the straw is fully submerged that the reduction in air pressure caused by 'sucking' means that atmospheric pressure pushes down on the liquid in the glass which then pushes it up the straw.

But what mechanism causes the liquid to be sucked up when air is also present and what physics can I use to determine the differences caused by different straw diameters, air flow and pressure?

I am doing a HNC mechanical engineering in the UK and currently studying the fluid mechanics module.

I am about to measure air flows but just wanted a sanity check that I am on the right lines.

Thanks in advance!

Homework Equations

Bernoulli’s equation

Poiseuille equation

Navier-stokes equations

The Attempt at a Solution

So far I think the liquid is en-trained into the air flow and up the straw due to the shear forces on the liquid because of the air flow. However the liquid is not easily transported up the straw like when it is fully submerged, due to gravity on the liquid in the absence of a sealed vacuum, adhesion of the liquid to the surface of the straw and the cohesion of the liquid causing a greater mass and greater surface area in contact with the straw wall causing a greater force required to draw it up. Also the surface tension of the liquid means the air flow struggles to en-train the liquid as the air molecules don’t want to ‘stick’ to the water molecules.

If a larger diameter straw is used then there is more surface area for the liquid to adhere to and more open space for the air to bypass the liquid and travel up the middle of the straw.

I have written this in a descriptive way as I am currently trying to visualise the problem and work out exactly what needs to be solved.

Air velocity is key is think, the higher the velocity the more successful one will be in causing the liquid to travel the length of the straw.

 

[haruspex]

Consider a straw with a number of bubbles in it.
Surface tension will stop the liquid falling down by the side of a bubble, if the straw is narrow enough (how narrow?).
The bubbles will reduce the weight of liquid in the column, making sucking easier.
Each bubble will have a lower pressure than air pressure, but greater than in your lungs. What is the relationship between that and the bubble height?
The surface tension at the upper meniscus of a bubble will cancel that at the lower meniscus, right? So I don't see that this makes it harder.

 

[rallyka2001]

Hi Haruspex, thanks for your reply!

When you say bubble height, do you mean actual diameter of the individual bubble or the height relative to the ground?

 

[haruspex]

Hi Haruspex, thanks for your reply!

When you say bubble height, do you mean actual diameter of the individual bubble or the height relative to the ground?

I meant height from bottom of straw. For simplicity I was thinking in terms of identical bubbles. What determines the size of each bubble is another interesting question.

 

[rallyka2001]

Ah, ok. I was looking into LaPlace pressure which talks about the size of the bubble and smaller diameters having higher pressure due to the 'pull' of the surface tension. Maybe that is getting ahead of myself?

Ok, so each bubble will have a lower pressure than air because it is being generated in a low pressure area. This means that atmospheric pressure will 'push' the bubbles up the straw because the surface tension creates a seal within the straw. If this seal is broken the liquid will fall back down.

So to answer your question, (What is the relationship between that and the bubble height?) the lower the pressure in the bubble, the higher the bubble can travel up the straw because there is a greater pressure, therefore force, acting on the bubble.

 

[rallyka2001]

So if this force is great enough it will push the liquid high enough to reach your mouth.

 

[rallyka2001]

So if there is not enough air flow or air speed to make this bubble form then you cannot suck anything up the straw?

 

[haruspex]

each bubble will have a lower pressure than air because it is being generated in a low pressure area.

That was my thinking, but it might be wrong. As the air goes into the straw it is true, but then liquid comes in behind it and surface tension will pull that liquid up against the bubble, increasing the pressure in it. But this has no effect outside the bubble. The surface tension at the two ends of the bubble generates nearly equal and opposite forces.

the lower the pressure in the bubble, the higher the bubble can travel up the straw

The bubbles further up the straw will have slightly lower pressure because there is less weight of liquid above them.

 

[rallyka2001]

Thanks for you time with this! I hope you are finding it interesting, I certainly am.

Are you suggesting that one single bubble fills the straw diameter, so there is a top surface, bottom surface and a surface clinging to the cylindrical sides of the straw? So when you say 'a straw with a number of bubbles' these identical sized bubbles (simplified as you say) stack up in the straw?

so then the smaller the diameter of the straw the easier it is for these bubbles to form as there is less distance for the liquid molecules to travel to either adhere to the straw wall or cohere to other liquid molecules, thus forming the bubble and the seal required?

 

[haruspex]

Are you suggesting that one single bubble fills the straw diameter, so there is a top surface, bottom surface and a surface clinging to the cylindrical sides of the straw? So when you say 'a straw with a number of bubbles' these identical sized bubbles (simplified as you say) stack up in the straw?

Yes.

the smaller the diameter of the straw the easier it is for these bubbles to form

I don't know that it is easier for them to form, i.e., that it is easier for air to get into the straw. The opposite might be the case. But in a wide straw the bubbles would not be able to block the liquid above from sliding down one side of the bubble. Now there's an interesting question: what is the minimum straw width?