Surfaces of Spinning Liquids
The interesting and fascinating curved surface.
What?
For a spinning liquid, what will be the shape of the surface? Why? If there are two kinds of liquids in the container, what will be the shape of the interface? Will be it the same as only one liquid?
How?
Experiment Equipment: Spinning table and liquid container
Manually rotate the spinning table, look carefully for the shape of liquids interface.
×Experiments demonstration
post-producing
Why?
With only one liquid in the container, while the spinning reaches steady state the liquid surface shall be an ‘up-concave paraboloid’.
×Think...
When the liquid is spinning at angular velocity 
Consider a small mass 
When there are two liquids, the oil water interface will form a special ‘down-concave paraboloid’. After a certain period of time, this ‘down-concave paraboloid’ will change back to the normal up-concave paraboloid. So the ‘down-concave paraboloid’ is a transient phenomenon. What is the cause of this phenomenon?
In the case of two liquids, the oil density is smaller than water, so the oil will float on top of water. Moreover, the oil is more ‘sticky’ than water that is the main reason for the inverted paraboloid. When we set the table into rotation, the cylinder rotates with the table immediately. However the liquids inside are still in steady. The out most liquid molecules in contact with the cylinder shall rotate with the cylinder first. These molecules drive the inner layer molecules, the inner layer molecules drive even inner layer molecules. Eventually, all molecules of the liquid are rotating with the angular velocity of the cylinder. However, water has smaller viscosity than oil, so it takes longer time for the water to rotate in the same speed.
Consider the extreme condition: when all the oil is rotating in the same speed while the water is still in rest. Now the oil surface has become a paraboloid. So, on the surface of oil the further from the rotation axis has the greater pressure. When the force acts to the water below, the oil water interface will deform from the horizontal surface to a ‘down concave paraboloid’.
But once the water is also rotate in the same speed, its surface has to be the up-concave paraboloid. The up-concave surface is now concaved more severer than the case where there is only water.
To explain this phenomenon, let’s consider another extreme condition: When the oil on top has stopped rotation (become stationary, so the surface shall be in horizontal), but the water is still rotating so the water surface (oil-water interface) must form an up-concave paraboloid. But why is it concaved more severely? Note that, the stationary oil is on top of water, which gives a static pressure 
In this experiment, the observation shall be the combination of these two extreme conditions.
Questions
- Put a transparent container on the spinning table with one liquid inside and set it on rotation then observe the shape of liquid surface. Is there any difference when increasing the rotation speed? What will be the case when there is acceleration (start up or stop down)?
- Put a transparent container on the spinning table with two liquids inside and repeat the above observation, what will be the shape of the interface?
About the Experiment
- Take the rotation speed, the coefficients of viscosity, the volumetric ratio of two liquids, and the diameter of the container as experiment parameters. So we may study their behaviors and reactions quantitatively.
Reference
Producer
v.1 Mr. Zeng （曾前助理）
Advisor
Ching-Chi Chu （朱慶琪）
Written by
Ching-Chi Chu （朱慶琪）
