MadSci Network: Physics

Re: Fluid Flow and the Viscosity of Wallpaper paste

Date: Tue Mar 20 23:35:52 2001
Posted By: Matthew Buynoski, Senior Member Technical Staff,Advanced Micro Devices
Area of science: Physics
ID: 984674333.Ph

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 

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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