Hi Mr. Clements, you ask a very intriguing question! Starting from the most basic concepts, we know that the liquid in the syringe would be far less compressible than the trapped air. Next, we have to consider what it means to expel the liquid in the syringe; basically, we need to apply enough pressure to the plunger so that the surface tension of the liquid in the syringe is overcome, allowing the liquid to flow out of the tip. Whether or not air is trapped in the syringe, the liquid should have the same surface tension. So, if we compare the air-trapped to the no air-trapped case, as long as one is pushing slowly, one will be required to press on the plunger with the same amount of force.

The important point, however, is that there is a finite flow from the nozzle. If I press really hard and fast on the no-air syringe, I will not compress the liquid and will not really be able to push much harder once I hit the max flow rate. If I press really hard on the syringe air, once I hit the maximum flow rate, I can still put additional energy into compressing the air. This is the kind of case where you will be able to have more plunger "play" and you will be able to push harder than in the no-air syringe.

This might change the “profile of the applied force” or the “total force over time”, but it would not change the maximum force needed to expel the liquid. For practical purposes, we can say that liquids are incompressible, and gasses are compressible. If there was only liquid in the syringe, the force you apply to the plunger would immediately be translated into moving the liquid out of the syringe. If there were gas in between the plunger and syringe, some initial force would go towards compressing the gas, but once the gas was compressed to a pressure equivalent to that needed to move the liquid (which likely would not require much force unless the syringe were clogged), the liquid would move out of the syringe just as it did before.

Consider 2 syringes. In Syringe A, air is trapped between the plunger and the liquid. In Syringe B, the plunger is in direct contact with the liquid. In both cases, assume that we are pushing out the liquid to the open atmosphere, e.g., we are displacing liquid to an open beaker.

Assume that the liquid volume in Syringe A is the same as the liquid volume in Syringe B. You need to apply enough pressure on the plunger to overcome atmospheric pressurehe syringe. Both the liquid and air have viscous forces that resist flow. Since you have the same amount of liquid in both syringes, then the viscosity of air determines the extra pressure required for Syringe A. In short, you do need to apply more force to Syringe A, though this extra requirement is probably very small as the viscosity of air is 2 magnitudes smaller than the viscosity of water in room temperature.

You proposed the idea that Syringe A requires more force to push the liquid out because air pushes back on the plunger. In fact, the liquid also pushes back on the plunger in Syringe B, and this is quite evident if you use a highly viscous liquid (try honey). The compressibility of air itself does not add to the pressure requirement of pushing the liquid out of the syringe. As you increase pressure, the volume of air will start to decrease. However, you can only continue to compress air until you reach the pressure requirement determined by the atmospheric pressure and the viscosity of the fluids inside the syringe.

I am not completely familiar with the setup of how a syringe works, so I cannot fully answer your question, although I can take a stab at what I understand the mechanics to be: a syringe consists of a piston (the plunger) pushing a fluid, and a tiny hole in the other end (the needle). Forces of friction and surface tension mean that there is a minimum pressure that is needed in order to force liquid out of the hole and down the needle. If you cannot exert that much pressure, then no liquid will be ejected through the needle.

Having an air bubble between the piston and the liquid means that pressing on the plunger will exert pressure on the air, which will in turn exert pressure on the liquid, instead of the plunger exerting pressure directly on the liquid itself. Because gasses are compressible and liquids are not exerting pressure on the liquid will result in all of the force applied by the plunger being applied to the liquid in the needle, but exerting pressure on the gas will cause the gas to compress, and only some of the force will be conveyed to the liquid initially. However, press hard enough, and you will still be able to get the liquid out through the needle.

So, in short, yes, I would expect the amount of force you need to increase. If you have a syringe, you can, however, conduct this experiment yourself, so I would recommend testing it and not take my word for it!

Your question reminds me of a chemistry professor in college who asked me about why liquid flowed faster from a pipet if one blew out the liquid instead of letting it run out by itself. I didn't have any answer, but now I'd say that one exerts a 'blowing' force in addition to the force of gravity, when blowing the liquid out of the pipet.

My mind was shocked at injecting air from a syringe, but of course you're not injecting it into a living creature.