|MadSci Network: Physics|
Hello, Alice! Two points up front, and then we'll get into some of your specifics. First, you should read section 3 of Chapter 2 of Bird, Stewart, and Lightfoot's "Transport Phenomena". The section is titled 'Flow through a circular tube' and has immediate relevance to what you are doing. The mathematics here includes some calculus; if you are not familiar with that, consult your instructors for help. Second, if the wallpaper paste you were using is anything like I'm familiar with, it is not, strictly speaking, a fluid, but a suspension of particles (of paste) in a fluid. This is a two-phase material, and they are *far* more difficult to understand from a theoretical point of view. The concept of 'viscosity' is not necessarily valid for two-phase materials; it's not even valid for some single-phase materials (so-called non-Newtonian fluids). This means you have actually set yourself quite a difficult task, perhaps more than you expected. By now, you may be the world's expert on this particular paste, since you've done experiments on it. I'd advise working with a single-phase fluid, perhaps a heavy motor oil, instead of a suspension, and control the fluid properties by dilution with some safe solvent, or a much lighter grade of oil such as that used for sewing machines. Do not use flammable organic fluids (e.g. toluene) without access to a fume hood and suitable protection equipment such as gloves, arm guards, face mask, fire extinguisher, etc. That said, let's go through your descriptions of what you've done, and the embedded questions, and see if I can add anything or supply some suggestions. Alice: "I am doing an A-level investigation into fluid flow and the viscosity of wallpaper paste. I have made up pastes of different thicknesses and have measured the time taken for the fluids to move down a tube. I have found some results that I can't quite explain myself and I was hoping that you could help. Firstly a thin tube caused the fluid to move slower down it than a thicker tube of the same length, also I know why fluid in the middle of a pipe moves quicker than that of the sides. However for the more viscous liquids once the majority of the fluid has moved out of the middle of the tube, some of it is still left at the sides and this takes alot longer than the rest of the fluid to move down the pipe. Is this because of the amount of the fluid left and is there a formula that relates the thickness of the layer of fluid left and its rate of flow. Mad Scientist: There are theoretical treatments of falling films. See Bird, Stewart, and Lightfoot, Chapter 2, Section 2, 'Flow of a Falling Film'. Falling films can get very difficult, especially if any wave action occurs at the upper surface. In your case, I also suspect that surface tension may play a significant role for the remaining material, especially if the tubes are small. Try putting small amounts of surfactant (soap, e.g.) in the pastes and see if this increases the rate at which the last parts "sticking" to the wall slide out faster. If the material remaining is not in a film but has broken into droplets, then it is likely that surface effects are not negligible and the wetting properties of the tube material by the fluid are also important. Try different tube materials and see what difference that makes. Alice: Also I discovered that after adding a certain amount of wallpaper paste powder to the water,adding more didn't have as much effect on the viscosity of the fluid. I was wondering whether this was because the water had become saturated with the powder or if it was something to do with the way the powder bonds with the water in order to form a paste. I would really appreciate it if you would be able to answer my questions... Mad Scientist: I suspect (but not having seen the exact mix, this is a guess) that what has happened is that the powder absorbs some water, and eventually a point arrives at which you have drawn up all the free water and have lost the lubrication effect of the free water between the powder grains and between the grains and the tube walls. So long as you are going out and using difficult fluids, you might try something completely different. If the particles of the dry powder are small enough, they may act quite fluid-like (but not exactly) in some ways. Perhaps you can grind your powder to several different sizes and correlate particle size to how the dry material flows through the tube. You may have to do measurements of particle size in a microscope, but it's an interesting expt. Another interesting two-phase experiment is to create a "fluidized bed". In these, a fluid is forced upwards through particles. A very gentle steady flow of air may suspend your powder, or perhaps you can use glass beads and flow water through them. There are some very fascinating and varied wave phenomena that can occur in fluidized beds . You will need a transparent tube, of course, and some sort of flowmeter/flow controller valve for the input fluid.
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