# Which of the two events will occur first

Consider a bottle partially filled with water and it is sealed from everywhere so that no air can enter or exit from bottle.Now make a small hole at the bottom of the bottle and hang it vertically so that hole faces downward direction. As we know bottle is sealed from everywhere else so the hole is the only place from where entry or exit of air or water is possible.Now two events will occur one after another repeatedly

1. a drop of water came out from hole due to gravity and falls down on ground
2. a bubble of air (or air)wil enter in bottle through hole and moves upward against the gravity and mixes with the air present at the top of liquid in bottle.

Now i know the reason for these two events to occur just because to maintain atmospheric pressure of air in bottle and due to gravity.But the thing in which i get confused is that which of the two events will occur first? I tried this experiment myself but not able to figure it out.I personally feel that event1should occur first

• Why is it even necessary for a bubble to enter the bottle at the bottom? Why can't a drop (or drops, or stream) come out the bottom with no air entering? Commented Dec 5, 2018 at 0:25
• @ChesterMiller if the hole is not very big then this will happen for example a hole of half milimetres is good to do this.Now this process will not be spontaneous if both the process will not take place because pressure cannot decrease or increase on its own without changing temperature or applying external force .Now gravity pushes the water drop outside and due which volume of water in bottle decreases and that of air increase without any increase in mass of air present in bottle due to which pressure decreases and hence a suction is created and air is pushed inside Commented Dec 5, 2018 at 1:47
• Also if hole is too much small then surface tension will take care of gravity Commented Dec 5, 2018 at 1:48
• Even if the pressure in the head space decreases, the hydrostic pressure should more than offset this so that water can continue to flow out(at least for a while) without air flowing in the bottom. Commented Dec 5, 2018 at 2:06
• So you are talking only about very small holes, right? Commented Dec 5, 2018 at 2:20

It depends on the diameter of the hole and the surface tension of the fluid in contact with that hole. For a small hole and/or high surface tension, the liquid sags out the hole and breaks off as a droplet; the remaining liquid recoils back into the hole and folds itself into a bubble which floats upwards. For a large hole and/or low surface tension, the sagging liquid and the rising bubble can squeeze past each other in the hole and the liquid dripping and air entry can occur simultaneously. This is called two-phase flow and its onset as a function of hole diameter and surface tension can be predicted with a mathematical tool called a similitude parameter.

• First of all it is not liquid which recoils back into the hole it is air which is sucked inside in form of bubble . I am talking about not too much big not too much small bubble i am talking about a hole of size in which can happen (like half a milimetre of diameter in case of water ) Commented Dec 5, 2018 at 1:57
• you will see liquid recoil if you watch this process through a strobe microscope, as I have. for a half millimetre hole, the flow will be assuredly single-phase: liquid out, air in, liquid out, air in, etc. Commented Dec 5, 2018 at 2:03
• so which of the two will occur first Commented Dec 5, 2018 at 2:17
• liquid protrudes from the orifice, then it breaks off and forms a drop, the meniscus retracts back into the orifice, forms into an air bubble, breaks off, and rises up through the liquid. Commented Dec 5, 2018 at 6:45

Here are three demonstration photos below:

• In the first one is of a plastic bottle with the 20mm hole subject to normal turbulence as the down-facing surface jitters. Water flows and air bubbles enter the bottle.

• In the second photo, a paper towel is cast over the hole. Now, both water and air can pass through the paper towel, but only water drips until the internal pressure does not allow it to drip further. Then, dripping stops as in the photo.

• In the third photo, I have pressed the bottle against the wet paper towel, but have left a small gap on one side, big enough for air to pass through provided you keep shaking the bottle slightly. With the bottle still and the hole small enough, no bubbles flow.

The key here is instability at the surface of the hole. If the surface of the water at the hole is calm enough, then the water will drip a little and soon stop flowing. No air will bubble through. It would indeed appear that the surface tension of water is high enough to prevent intrusion by air if conditions are calm enough. If the surface is turbulent enough, bubbling will occur immediately. If bubbling happens, then it is almost certain that a water droplet will have to fall, due to the discontinuity created by incursion of the air bubble. However, water sipping away does not imply a bubble.

• Try with a sealed bottle without shaking or pressing the bottle it with a smaller hole about 5 mm . Commented Dec 5, 2018 at 14:05