# Pressure increase with air bubbles in catheter

I perform experiments that make use of a syringe fluid infusion pump that infuses fluid through a catheter to a desired target.

Below is a representative schematic of my setup with the infusion pump connected to a pressure transducer and catheter that empties into a reservoir as an example.

I often notice that air bubbles exist within the small diameter catheter initially but can be cleared with sufficient infusion. When I look at the measured pressure with time, the period with air bubbles present in the catheter has elevated pressure followed by a rapid fall in pressure down to its stable steady-state once they have been removed.

1) I am curious what my be happening within the catheter that causes this kind of pressure increase/decrease with the air bubbles. Wouldn't the air bubbles push on the water molecules in the same fashion, thus transmitting the pressure to the transducer or are their increases in pressure due to material interfaces?

2) If the air bubbles were replaced with vacuum, would the same observation be observed?

More of a question based on my curiosity.

Thank you for you time

I can think of a few effects in play:

First, when there are bubbles in the line, the "effective density" of the liquid will be lower - so if there is a drop $h$ from the infusion pump to the level of the liquid in the reservoir, there will be a pressure difference between the pump and the atmosphere of $\rho g h$. If $\rho$ drops, so does the pressure "pull" from the liquid, meaning the pump has to work harder.

Second, there may be surface tension effects. If you are trying to push a bubble into the liquid, the curvature of the air bubble and the surface tension of the liquid will cause an effective increase in pressure (in the bubble, and thus in the upstream system). The smaller the diameter of the bubbles, the bigger this effect will be (pressure difference is given by

$$\Delta P = {\rm{\frac{force}{area}}} = \frac{2\pi r \sigma}{\pi r^2} = \frac{2\sigma}{r}$$

Where $\sigma$ is the surface tension - which creates a force per unit length along the circumference of the bubble, and that force is countered by the pressure that works across the projected area of the bubble.

There might be other surface effects inside the tube as surface tension will interact with the air/liquid interfaces; in principle, these things ought to cancel (where one liquid/air surface might create "push", the next air/liquid interface might create "pull") but that's not necessarily true.

I suspect that surface tension is the main culprit - but without seeing the exact setup that is hard to confirm.

• Thank you for breaking this down! One thing to mention is that during the pressure increase period at the beginning of the infusion, there is some delay before the bubbles actually start to move down the catheter. I guess this is likely the need for a high enough force by the pump to overcome the surface tension force. Oct 12, 2017 at 21:47