The Project

 

In this project we're trying to understand the motion of fluid surfaces driven entirely by capillary forces.

There are two main systems we'll focus on. The first is the rise of liquid in a circular capillary tube. This

problem has been studied since at least the 1950's and many groups have conducted experiments with

this system. Our first goal is to gather data on the height of the fluid in the tube as a function of time

and compare it with existing theory.

 

An explanation of the basic theory can be found at:

 

Explanation of Differential Equation

Phase Plane of Differential Equation

Short Time Analysis

Derivation of Laplace - Young Equation 

Error Analysis 

 

To gather data, we use a high speed camera. The camera is turned on, the tube is lowered into a

pool of silcone oil, and we film the system as the fluid rises. A typical video can be found below.

 

Video of a Capillary Tube entering a pool of Silicon Oil

 

 

 

 

The second focus of our study is on the rise of fluid in a wedge. For this experiment, we use glass microscope

slides held together at an angle. Again, the high speed camera is used to gather data. The setup is the

same as above, that is, the camera is turned on,  the wedge lowered into the fluid, and the motion of the

surface filmed. For this system, we are developing the theory. A typical video is shown below.

 

 

Video of a Wedge entering a pool of Silicon Oil

 

 

Thoughts...

 

There is now a section in the Explanation of Differential Equation page to explain the non-zero initial velocity.

Good! Thank you.

 

First thought, I took a look at the calculation you did to see what value of r would give the correct

steady-state, using all other values from Brittin. There must be an error somewhere, the r you compute

is smaller than the actual r, yet using the actual r gives a bigger value for the steady-state. Since

the steady-state is proportional to 1/r something is screwy...

 

Anson and I redid the experiments with the silicon oil and water. We tried three different approaches for each liquid. We frist tried aligning the camera while using an untampered tube, aligning the camera while using a disinfected tube, and aligning the camera while using the pre-wetted tube with silicon oil. In general the results were very similar to our previous experiments, with the exception of the pre-wetted tube and the water experiment,. We think that it is possible that the liquid could have been rising very slowly and that we should have let it run for a longer period of time. We suggest redoing the experiments with an untampered tube while allowing for a longer recording to see if it is possible for the experiment to reach closer to the expected steady state.  

 

 

More later...

 

Capillary Tube Experiments with Silicon Oil

Capillary Tube Experiments with Water

Capillary Wedge Experiments with Silicon Oil

Sponge Experiments

Sand Experiments 

 

 Slide Show Presentation (08/07/07): Capillary Presentation.ppt