Introduction Hands-on homework (H2O) kits
John Selker, Oregon State University
selkerj@engr.orst.edu
These kits are available to be ordered! Or build your own-this is what you will
need:
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(1) 400 mL beaker
(1) sponge
(10) 4.5 mL cuvettes
(10) cuvette covers
(1) bag 30/40 sand
(1) vial blue dye
(1) 1 m tubing
(1) barbed connector
(1) plastic hose clamp
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(1)
(6)
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(1)
(2)
2 mL cylinder
capillary tubes (2 each of 3 sizes)
culture tube
size 0 stopper
25 mL cylinder
funnel
30 cm acrylic pipe
3-hole size 7 stopper
square nylon mesh
These tasks facilitated using these kits are meant to let you experience the basic physical
processes that will be discussed in the class. I hope that you will think long and hard
about what these simple experiments are telling you. Many of these tasks will be the
basis for quantitative calculations. All you will need to carry these out, in addition to the
materials that I provide, is a source of tap water, a ruler, and a watch. Although used for
a number of years, PLEASE feel free to let me know how to make them work better for
the next time we use these. They should be fun, informative, and useful in developing
your intuition for how unsaturated porous media works.
Overview of HOH’s
Study of Capillary Forces
Develop intuition for capillary pressure and water retention: Sponge
Quantitative understanding of capillary attraction and hysterisis: Micropipetes
Quantitative understanding of surface tension: Soapy water and Micropipetes
Flow in Porous Media
Flow in single capillary tubes: Poiseuille flow in capillaries
Darcy’s Law in sands: Column experiment with two sands
Solute Transport
Observation of dispersion in sand systems: Sand columns with blue dye
Suggested approach: Each person should do their experiments independently, taking all
data from their own apparatus. Some have found that two sets of hands is helpful in
carrying out the solute transport experiment, which is fine, but make sure tht ech person
does the full analysis independently to get the message of the exercise. Working on data
with discussions in groups, just as with any other homework, is a good idea when the
going gets tough. As in other homework, qualitative interpretation is key: what do the
(correctly calculated) numbers suggest? Are they reasonable? On what basis? There
need be no more than one paragraph responses to each question on the handouts (to keep
you from feeling that you must write about every detail of what you observe).
HOH Homework #1: The Sponge of Mystery
This set of tasks is intended to start you thinking about hydrostatic forces and the
retention of liquid by porous media.
1.
Hydrostatics in pure water.
Wash your beaker and fill it to the 400ml mark with something you want to drink.
a.
What is the water pressure at the top of the water surface? Why?
b.
What is the water pressure at the bottom of the glass of water? Why? (Please be
careful with the units you use in expressing pressure.)
c.
Draw a plot of water pressure versus height in the glass of water.
d.
Drink half of the liquid and repeat a-c.
e.
Finish the drink and wash the beaker. Comment on how your result would have
been effected by the sugar content of the drink you selected (hint: assume the
sugar changes the density).
2.
Capillary forces.
Refill your beaker with water and find your sponge.
a.
Dip the narrow edge of your sponge in the (it should just fit in). Only put the first
5 mm of the sponge in the water so that it might soak up water. Hold it so that it
keeps about 5 mm of the sponge in the water. Continue this for 3 minutes.
i.
Doesn't this lifting of water upward into the sponge defy gravity? Try to describe
the physics of what made the water rise in the sponge.
ii.
By pinching the sponge between your fingers going from the top of the sponge to
the bottom as a way to measure water content, make a qualitative plot of the
moisture distribution in the sponge.
b.
Dip the entire sponge in the beaker, wait for the sponge to take up water, then lift
the sponge so that only the last 5 mm is in the water, just as in step 2a. Now the
sponge is draining water back into the beaker.
i.
Now repeat parts 2a i and 2a ii, drawing the plot of moisture content on the same
figure but with a different color pen. Try to explain why the two moisture
contents aren't the same.
ii.
Do you think that if you had waited 24 hours that the two moisture profiles be the
same (assuming that we didn't allow evaporation from the sponge.)?
iii.
Plot what you think the water pressure is from the bottom of the glass of water to
the top of the sponge.
3.
Hydrostatics and Capillarity.
a
Get a pan big enough to lay your sponge in. Lay the sponge flat in a pool of water and
carefully lift the sponge out while keeping it flat (a spatula might be helpful here).
a.
b.
c.
How much water came out? How long did it take to stop dripping?
Turn the sponge on its edge by holding it by its longest edge. Did more water
come out? Why? How long did it take to stop dripping compared to above?
Now for the last step: Turn the sponge so that it is hanging by its shortest edge, by
holding it by its shortest edge. Did more water come out? Why? About how long
did it take to stop dripping compared to a. and b.?
a.____________________________________
b.____________________________________
c.____________________________________
HOH Homework #2: Capillary tubes
In your homework kit you will find three capillary tubes. Each has a different diameter.
Please follow the following directions to explore the issues of La Place's equation and
capillary hysteresis.
Procedures: (be careful: the tubes MUST BE DRY, so don’t “play with them” before the
test)
1.
Hold the tubes vertically throughout this procedure. Fill your beaker with tap
water. Dip the very end of each tube (as little as possible) into the water. When it
has filled to an equilibrium height (wait a minute or so), pull the tube from the
water and measure the height of the capillary rise.
2.
Hold the tubes vertically throughout this procedure. Suck on the tube while the
lower end is in the beaker of water to fill it completely with water. Now with the
lower end of the tube in water, let the tube drain to equilibrium over at least 1
minute. Remove the tube from the water and measure the distance from the
bottom of the tube and the water level in the tube.
3.
Repeat steps 1 and 2 now that the tube has been wetted.
4.
Repeat step 1 holding the tube at a 45 degree angle.
5.
Add a spoon of drops of dish washing liquid to your beaker of water. Mix the
solution thoroughly and repeat steps 1 and 2.
(You may have to blow the water out of the tubes between tests)
Table of Measurements - in cm
Tube
Red
Orange
White
Procedure 1 - Wetting
Procedure 2 - Draining
Procedure 3a - Re-wetting
Procedure 3b - Re-draining
Procedure 4 - 45 deg
Procedure 5a - Soap wetting
Procedure 5b - Soap draining
Excercises
1 a. Given the results of steps 1 and 2, is the minimum contact angle that must have
existed between the water and the wall of the tube zero in the initial wetting stage?
b. Compute the contact angle for initial wetting each tube using the results of
procedures 1 and 2 (expain why a zero contact angle assumption is reasonable for
the drying stage).
c. Since we are using pure clean glass in this experiment, without surface defects or
contamination, speculate on the contact angle you might expect in typical soils.
2. Given the results of procedure 3, was there still some water film on the walls of the
tube when you re-wetted? What makes you say this? What about the re-draining
step: did you see a change? Did you expect a change? Why/why not?
3.
Do the results from procedures 3 and 4 agree physically? Explain quantitatively.
4.
Compute the surface tension of the soap solution using the results of step 5. Are the
values consistent between the various capillary tubes?
Tube Red
Initial Contact Angle
Soap Solution Surface
Tension
Orange
White
HOH Homework #3: Permeability
In this set of experiments you will explore Darcy's Law from the perspective of a single
capillary tube, and a saturated column of sandy soil.
1.
Parts: three capillary tubes and the graduated reservoir tube
Attach the cylindrical plastic reservoir to the top of each of your three capillary tubes in
turn. Measure the time required for between 1.0 and 0.1 ml of the reservoir to pour
through the capillary tubes depending on the tube. Select a volume such that the time of
the experiment is about 1 minute. Be careful to measure the height of the water surface
above the bottom of the capillary tube to obtain the total potential across the flow path.
Using the flow versus radius relationship of Poiseuille, compute the radius of the
capillary tubes. Compare your answers to those values found for the radii in the capillary
rise experiments (some people didn’t compute the radius using the capillary rise
experiment: now’s your time to do this if you didn’t on the last go around!).
3 bonus pts: run the same experiment with the tubes held between two bags of ice water.
Calculate the apparent change in viscosity between using room temperature water and
water at 0 deg C
2 MORE bonus pts: run the same experiment with the tubes pushed up into the
reservoir so that the total head across the system is lower. Show that the flow is linear
with total head loss.
2.
Parts: 30 cm acrylic tube; #7 white rubber stopper; bag of sand; 0.75 m flexible
vinyl tube; white plastic tubing connector; nylon mesh.
Open one of the holes the white rubber stopper. Plug the bottom of the plastic column
with the white rubber stopper with the white nylon screen tightly wrapped around the
stopper so that the sand cannot enter the open hole in the stopper. Pull out the stopper
and carefully trim the nylon mesh into a circle that is bigger than the top of the stopper,
but small enough to not leave any mesh hanging down from the column when installed
(about 5 mm greater radius than the top of the stopper). Reassemble the mesh and
stopper into the tube. Fill the clear plastic pipe about 2/3’s of the way with the sand
provided. Set up the sand column in a stable situation so that you do not have to hold it
upright in your hands (you could tape it to the edge of a door, or use a rubber band
around the handle to hold it). Push the white plastic tube fitting into the bottom of the
stopper and attach the flexible clear plastic tube, which has been filled with water, to the
bottom of the system so that the open end of the flexible tube is even with the bottom of
the stopper. Put the open end of the flexible tube in a beaker full of water. Elevate the
vinyl tube from the bottom of the column to the height of the top of the column so that
the column fills with water. Now clamp the flexible tube closed and drop the outflow
pipe to be even with the bottom of the column. Pour water in the top of the column until
the water is about 1 cm from the top. Now open the clamp and measure the time for the
water to fall from the top of the column to the top of the sand (stop by clamping the tube).
DON’T let the water level fall below the top of the sand or it will desaturate, never to be
fully saturated again! Repeat. Now do the same experiment, but put the outlet 15 cm
below the bottom of the column, then 30 cm below the bottom of the column. In these
experiments make sure that the vinyl pipe stays full of water by letting the water flow out
of it upwards.
a.
b.
c.
Compute Ks for each test based on each of the three experiments.
Based on the value obtained, using the Poiseuille-law, estimate the average pore
side in the sand.
Based on this average pore size, how high would you expect water to rise in this
sand due to capillarity?
HOH Homework #4: Solute Transport Experiment
The goal of this homework is to make the processes of solute advection and
spreading clear to you.
1.
Prepare your concentration standards. Prepare 1:4 dilutions until you have four
vials filled with successively more dilute mixes. Here’s how I would make my first two
dilutions: Take the blue dye fill one small glass vial with the dye and pour it into my
beaker. Pour three more vials of water into the beaker. Mix well, and remove one vial
full of the 0.25 Co dilute solution. Add 9 more vials of water to the beaker, mix well, and
fill one more vial with this solution to obtain your 1/16 Co solution. Proceed carefully to
obtain dilutions of 1:64 and 1:256.
2.
Take your large plastic tube and assemble the screen, stopper, and outflow pipe as
in the conductivity test. Fill the tube two-thirds with dry sand.
3.
Saturate the sand as in the conductivity experiment. This time be careful t
measure how much water was required to saturate the sand: this is your system’s pore
volume.
4.
Pour one vial of pure blue dye onto the sand with the water table just at the top of
the sand. Now, counting vials, continue to pour vials of water onto the system to push
the dye through the sand.
5.
As soon as the dye become apparent in the outflow, collect the outflow water in a
vial and compare it to the dilute solutions. Estimate the concentration in each effluent
vial.
6.
Plot the dye concentration versus outflow volume with outflow volumes
expressed in “pore volumes.” To understand this, say the column had 300 mls of water,
and the vials hold 5 ml. Then there would be 60 vials per pore volume. Thus, each vial
applied would be 1/60th of a pore volume.
7.
Fit the standard CDE Gaussian solution to your outflow data and estimate the
longitudinal Dispersivity of your sand.
8.
Comment on the results of this experiment.
HOH Homework #5: Water Retention Curve Exercise
1.
Put both mesh screens over the stopper and push the stopper into the plastic pipe.
Use a tabletop to push the stopper in as far as you can.
2.
Measure 100 mL of sand into the beaker. Tap the beaker repeatedly on the
counter and add sand until its volume stabilizes to 100 mL. Notice that packing strongly
affects porosity. Pour the sand in the pipe and tap the pipe with a wooden spoon or
another object that will not crack the pipe until the sand level stabilizes.
3.
Slide the white crimp clamp on the clear tubing and insert the barbed fitting into
one end and the funnel end into the other with the white clamp in the middle of the
tubing. If the barbed fitting is not snug, cut a little off the end of the tubing and
reconnect. Fill the tubing and funnel with water, taking care that there are no air bubbles
in the tubing or funnel stem. You may tilt the pipe slightly while inserting the barbed
fitting. Fill the funnel to the top with water.
4.
Readjust the column into a vertical position. Open the clamp to let the water enter
the sand from the bottom up. Position the water level in the funnel at the same height as
the level of the sand, and let water enter until the water level is just above the sand,
making a shiny surface. To prevent bubbles in the system, keep the water level
somewhere inside of the funnel cone by adding water, recording how much water you
add. When the water is at the sand surface, close the clamp.
5.
Measure the amount of water it takes to refill the funnel to its initial water level.
Add this to the amount of water you added to the funnel while the water was entering the
sand. This is the amount of water that entered the sand.
6.
Drain just enough water from the pipe so that the sand surface is no longer shiny.
Empty the graduated cylinder.
7.
Turn the sand filled pipe horizontally. Take the funnel off the end of the tubing
and place the end of the tubing level with the top of the flexible tubing. Undo the clamp.
Lower the tubing in 5 cm increments and let the water drip into the graduated cylinder.
At each increment, wait until the drips have slowed to less than one drip every 5 seconds,
and record the volume of water that was drained for that increment. Watch and record
when air enters the vinyl pipe. When air enters the pipe, that is the end of the
experiment. The experiment should end when 50-60 cm pressure is applied.
8.
Estimate the mesh size of the screen based on the air entry pressure.
9.
Graph the water retention of the sand.