Colloids Laboratory
Wicking Flow in Porous Media
Performed: 10/27/10 & 11/3/10
Written By: John Willey
Group Members:
Andrew Adams
Ian Gregg
Abstract
The goals of this experiment were to determine the effect of capillary and gravitational forces
on several fluids, to test the Washburn equation with experimental data, to measure the
capillary action or the penetration of filter paper and to design a wicking flow assay. The data
fits the Washburn equation for capillary flow at different inclines. For wicking flow it was found
that the Washburn equation does not fit the data accurately in most cases. When dye
penetrated into a packed porous media it was found that the dye moved at a constant velocity.
In conclusion it is found that the Washburn equation predicts the capillary action in capillaries
better than it does for fluid penetration of a porous media, and when designing a wicking
lateral flow assay the movement of an analyte in a packed porous media can be approximated
by a constant velocity.
Introduction
There is a large need for testing assays that are cheap, fast and reliable. Lateral wicking assays
are a method of testing that meets all three of these criteria. Assays detect the presence of a
particular protein or another particular chemical species that would indicate a specific
condition is present. A famous example is the home pregnancy test, but there are others on the
market as well that test for different diseases.
To design a wicking assay, it is required to know how fast and how far different analytes will
wick along a piece of filter paper. This is because many tests require several different chemical
reactions to occur at different stages and the designer must know where to put these stages on
the wick.
This experiment allowed the study of fluid penetration in wicks and also considered the use of
the Washburn equation to predict distance covered by a fluid over time in both wicks (porous
media) and capillary tubes. Understanding fluid movement in different conditions will be
applicable in the design of wicking flow assays.
Capillary
Figure 1: capillary tube diagram
X
α
Fluid Trough
Theory
Capillary forces exist because of surface tension forces that act on a fluid. This force can be
modeled by the Young-Laplace equation.
∆𝑃 =
2𝜎 cos 𝜃
𝑅
Where ∆𝑃 is the pressure generated by the surface tension, 𝜎 is the surface tension of the fluid,
cos 𝜃 is the contact angle of the fluid to the capillary wall, and 𝑅 is the mean radius of the
capillary.
It can be seen that as the radius of the capillary decreases, the pressure generated by surface
tension forces increases. If the fluid is static, then there cannot be a pressure difference exerted
on the fluid. The force generated by surface tension must be counteracted by another force,
usually gravitational forces.
If the capillary tube is at an incline, then as the fluid rises in the tube it increases the weight of
the fluid in the capillary. Eventually the weight of the fluid will balance against the interfacial
forces and the fluid will become static. At this equilibrium the rise height can be calculated from
the condition that the net force on the fluid is equal to zero.
𝑋=
2𝜎 cos 𝜃
𝜌𝑔𝑅 sin 𝛼
Where 𝜌 is the fluid density, 𝑔 is the gravity constant, and sin 𝛼 is from the incline of the
capillary tube.
If the fluid is not in equilibrium the Washburn equation can be used to model the distance
traveled by the fluid over time.
If sin 𝛼 = 0
𝜎 cos 𝜃 𝑅 1/2 1/2
𝑘𝑤 = (
) ∗𝑡
2µ
If sin 𝛼 ≠ 0
𝑡=
8𝜇𝑋
𝑥
𝑥
(− ln (1 − ) − )
2
𝜌𝑔𝑅
𝑋
𝑋
Where 𝜇 is the viscosity of the fluid 𝑘𝑤 is the Washburn slope and 𝑋 is the total distance
traveled by the fluid in the capillary tube.
This experiment will test the validity of these equations for capillary tubes, and will test if they
can be applied to wicking or fluid penetration of a porous media successfully.
Experimental
The experiment was performed in three separate parts, capillary flow, wicking and designing a
lateral flow wick assay.
To observe capillary flow there were two capillaries prepared, one had a volume of 10 micro
liters and the other had a volume of 5 micro liters. These capillary tubes were set at different
incline angles in two different fluids. The fluids were de-ionized water and silicon oil. The
distance traveled by the fluid in the capillary was measured over time, along with the
equilibrium rise height when α = π/2 radians.
Wicking experiments were performed on nitrocellulose and whatman 41 filter paper. The paper
was cut into thin strips and allowed to dip into de-ionized water or silicon oil inside of a test
tube. The tube containing water was covered by a damp cloth, to prevent evaporation from the
wick. The distance traveled by the fluid on the wick was measured over time.
To design a lateral flow wick assay we measured the time required for both water and a dye to
travel along the wick. While designing the wick assay we used a pattern with varying lengths of
wick that met at a common point. The assay had four loading pads for the chemical species and
one sink pad, to encourage analyte movement. The assay was treated with a pH sensitive dye,
and a dilute acid and base were then loaded onto separate parts of the wick assay.
Results
A. Capillary Rise
Table 1: Theoretical Equilibrium Rise Height
10 micro liter capillary
5 micro liter capillary
Ethylene Glycol
3.5 cm
4.9 cm
Silicon Oil
1.7 cm
2.5 cm
Table 2: Measured Equilibrium Rise Height
10 micro liter capillary
5 micro liter capillary
Ethylene Glycol
3.6 cm
5.2 cm
Silicon Oil
1.9 cm
2.7 cm
Comparison of Measured to Theoretical Rise Height
Uncertainty in Height Measurements:
0.25 cm
√(0.25𝑐𝑚 ∗ 0.25𝑐𝑚) ≈ |(5.2𝑐𝑚 − 4.9𝑐𝑚)|
0.25 ≈ 0.3
Thus the difference between the measured and experimental data is on the same order of
magnitude. The theoretical rise height agrees with measured values.
Table 3: Measured Contact angle Cos (θ)
10 micro liter capillary
5 micro liter capillary
Ethylene Glycol
1.04
1.05
Silicon Oil
1.09
1.09
Another demonstration that the equilibrium rise height agrees with the experimentally
observed rise height is that the experimental value of the cosine of the contact angle (cos 𝜃) is
approximately one, which is expected when calculating the theoretical value.
Figure 2: plot of distance traveled by ethylene glycol over time1/2 in a 10 µL tube
Distance Travelled (m)
Ethylene Glycol in a 10 microLiter capillary
0.12
0.1
0.08
0.06
0.04
Experimental (alpha = 0)
0.02
Washburn (alpha = 0)
0
0
2
4
6
8
SQRT[ Time Elapsed (s) ]
The Washburn slope agrees with the experimental slope when Ethylene Glycol was tested in a
10 micro liter capillary tube. The experimental values are shifted downward; this is thought to
have occurred due to an initial timing error at the start of the experiment.
Figure 3: plot of distance traveled by ethylene glycol over time1/2 in a 5 µL tube
Ethylene Glycol in a 5 microLiter capillary
0.14
Distance Traveled (m)
0.12
0.1
Experimental (alpha = pi/2)
0.08
Experimental (alpha = pi/4)
0.06
Experimental (alpha = 0)
Washburn (alpha = 0)
0.04
Washburn (alpha = pi/2)
0.02
Washburn (alpha = pi/4)
0
0
2
4
6
8
10
SQRT[ Time Elapsed (s) ]
Figure 4: plot of distance traveled by silicon oil over time1/2 in a 10 µL tube
Silicon Oil in a 10 microLiter capillary
0.14
Distance Traveled (m)
0.12
0.1
0.08
Experimental (alpha = 0)
0.06
Washburn (alpha = 0)
0.04
0.02
0
0
5
10
SQRT[ Time Elapsed (s) ]
15
20
Figure 5: plot of distance traveled by silicon oil over time1/2 in a 5 µL tube
Silicon Oil in a 5 microLiter capillary
Distance Traveled (m)
0.12
0.1
0.08
Experimental (alpha = 0)
0.06
Experimental (alpha = pi/4)
0.04
Washburn (alpha = 0)
0.02
Washburn (alpha = pi/4)
0
0
5
10
15
20
SQRT[ Time Elapsed (s) ]
The experimental values of silicon oil are compared to the Washburn predicted values in
Figures 4 & 5. Silicon oil does not have a pronounced meniscus, causing difficulty when taking
the measurement at α = 0. This can be seen from the deviation from predicted values and the
experimental values that exist only when α = 0.
B. Wicking into Filter Paper
Microscopic Observations:
It appears from Figure 6 that the diameter of the average pore in nitrocellulose is of the order
of 5 microns. It also appears that the pores are finer and more regularly dispersed then the
pores found in whatman 41 paper. From Figure 7 the average pore diameter of whatman 41
appears to be on the order of 10 microns, and the pores appear jagged and less uniform then
those of Figure 6. The image depicted in Figure 7 appears to be striated and fibrous, while
Figure 6 appears soft and clumped.
Figure 6: Microscopic view of nitrocellulose paper
Figure 7: Microscopic view of whatman 41 paper
Figure 8: plot of distance traveled by de-ionized water over time1/2 in nitrocellulose
Distance Traveled (m)
D.I. Water penetrating Nitrocellulose
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Experimental
Washburn
0
5
10
15
20
SQRT[ Time Elapsed (s) ]
The experimental values of de-ionized water appear to penetrate at the rate predicted by the
Washburn equation. The initial kink in the experimental values at start up might be attributed
to initial wetting of the filter paper or experimental error due to timing.
Figure 9: plot of distance traveled by de-ionized water over time1/2 in Whatman 41
D.I. Water penetrating Whatman 41 Paper
Distance Traveled (m)
0.12
0.1
0.08
Experimental
0.06
Washburn
x = 0.003 t1/2 + 0.011
0.04
Linear (Experimental)
0.02
Linear (Experimental)
0
0
5
10
15
SQRT[ Time Elapsed (s) ]
20
25
The experimental data for de-ionized water penetrating whatman 41 demonstrates a
dependence on the square root of time. This is similar to the Washburn equation, except the
data is fit best by a line with a non zero intercept. This must be due to experimental error
because the fluid cannot penetrate the paper until after the experiment has started.
Figure 10: plot of distance traveled by silicon oil over time1/2 in Nitrocellulose
Distance Traveled (m)
Silicon Oil penetrating Nitrocellulose
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Experimental
Washburn
x = 0.004t + 0.018
R² = 0.994
0
5
10
15
Linear (Experimental)
20
SQRT[ Time Elapsed (s) ]
Figure 11: plot of distance traveled by silicon oil over time1/2 in Whatman 41
Distance Traveled (m)
Silicon Oil penetrating Whatman 41 Paper
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Experimental
x = 0.003t + 0.010
R² = 0.994
0
5
10
15
SQRT[ Time Elapsed (s) ]
20
Washburn
Linear (Experimental)
25
Silicon oil penetrating nitrocellulose (Figure 10) appears to follow a linear line on a plot relating
the square root of time to the distance traveled. The Washburn equation also shares the same
dependence on time, although the slopes and intercepts are different. Silicon oil penetrating
whatman 41 paper (Figure 11) appears to have a linear dependence on time.
Table 4: measured wicking equivalent pore radius
Nitrocellulose
Whatman 41
D.I. Water
0.53 µm
2.4 µm
Silicon Oil
0.44 mm
0.22 mm
The equivalent pore radius is highly dependent on what fluid is using, as the values found for
de-ionized water are three orders of magnitude different from those found for Silicon Oil.
Table 5: estimated wicking equilibrium rise heights
Nitrocellulose
Whatman 41
D.I. Water
28 m
6.3 m
Silicon Oil
9.6 mm
19 mm
It appears that the equivalent radius is smaller for water in the filter paper, which causes the
rise height to be higher. This is of course the case, since rise height is inversely proportional to
the radius of a capillary in the capillary model is being utilized to describe the wicking paper.
C. Lateral Flow Assay
Figure 12: moving front of de-ionized water on the lateral assay over time1/2
Distance Traveled (cm)
D.I. Water penetrating Wick Assay
6
5
4
x = 0.360 t1/2
R² = 0.989
3
2
1
0
0
2
4
6
8
10
12
14
SQRT[ Time Elapsed (s) ]
Flow through the packed membrane appears to follow the Washburn format, having the same
shape as the function x = kW t1/2. The constant kW is the Washburn slope, and depends on the
fluid and membrane properties. From Figure 12 the data has been fit to the Washburn format
which appears as a linear curve. The Washburn slope in this case would be 0.36 (cm/s)
Figure 13: moving front of dye on the lateral assay over time1/2
Dye penetrating packed Wick Assay, t1/2
Distance Traveled (cm)
5
4
3
x = 0.174 t1/2
R² = 0.953
2
1
0
0
5
10
SQRT[ Time Elapsed (s) ]
15
20
25
Figure 14: moving front of dye on the lateral assay over time
Distance Traveled (cm)
Dye penetrating packed Wick Assay, t
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
x = 0.007t + 0.730
R² = 0.992
0
50
100
150
200
250
300
350
400
450
500
Time Elapsed (s)
The dye does not appear to follow the Washburn format, as can be seen by the attempted fit
on Figure 13. The distance traveled by the dye appears to be proportional to time, not time 1/2.
Since the Washburn format is x = kW t1/2, it cannot be followed by the wicking dye as
demonstrated by the data collected. Apparently the dye travels in a linear fashion, as shown by
the fit line in Figure 14.
Figure 15: diagram of designed lateral flow assay, made of nitrocellulose
Loading
Pad
Sink Pad
Figure 16: wicking assay created, snapshots taken over time
Time
The diagram of the lateral flow wicking assay in Figure 15 was generated and is shown in Figure
16. A pH sensitive dye was placed on the test, which initially is yellow. After that an acidic
solution was applied to two loading pads, along with a basic solution (on separate pads). The
purple pads are the recipients of the acidic solution, while the light yellow pads are the
recipients of the basic solution. The larger pad that is only partially yellow is the sink for the
experiment. As can be seen, the acidic solution wicked towards the center of the assay and was
unable to continue. This is due to the basic solution counteracting the acid, preventing the acid
from activating the dye past the center of the wicking assay.
Sample Calculations
Radius of 5 µL capillary
𝑟 = √𝑉𝑜𝑙𝑢𝑚𝑒/𝑙𝜋
1,000𝑐𝑚3
√
𝑟=
= 0.0177𝑐𝑚
5.1𝑐𝑚 ∗ 𝜋
Theoretical equilibrium rise height
ℎ=
2𝜎𝑐𝑜𝑠𝜃
𝜌𝑔𝑟
𝑓𝑜𝑟 𝑠𝑖𝑙𝑖𝑐𝑜𝑛 𝑜𝑖𝑙 𝑖𝑛 𝑡ℎ𝑒 5 𝜇𝐿 𝑐𝑎𝑝𝑖𝑙𝑙𝑎𝑟𝑦
𝑁
ℎ=
2 ∗ .0208 𝑚 ∗ 1
𝑘𝑔
𝑚
965 𝑚3 ∗ 9.81 𝑠2 ∗ 0.000177𝑚
= 2.5 𝑐𝑚
Contact Angle
cos 𝜃 = ℎ 𝜌𝑔𝑟/2𝜎
cos 𝜃 = 0.027𝑚 ∗ 965
𝑘𝑔
𝑚 0.000177𝑚
𝑘𝑔
∗ 9.81 2 ∗
(0.0483 )−1 = 1.09
3
𝑚
𝑠
2
𝑚𝑠
Washburn slope for α = 0
𝑘𝑤 = √𝑟 ∗ 𝜎 ∗ 𝑐𝑜𝑠𝜃/2𝜇
𝑁
𝑘𝑤 = √0.000177𝑚 ∗ 0.0208 ∗
𝑚
1.09
𝑘𝑔
2 ∗ 0.0483 𝑚 𝑠
= 0.0077
𝑚
𝑠 .5
Washburn Equation when capillary tube is horizontal
𝑥 = 𝑘𝑤 ∗ 𝑡 .5
𝑥 = 0.0077
𝑚
∗ 1.45.5 𝑠 .5 = 0.0093 𝑚
𝑠 .5
Washburn Equation when capillary tube has rise
𝑡=
8𝜇𝑋
𝑥
𝑥
(− ln (1 − ) − )
𝜌𝑔𝑟
𝑋
𝑋
.5
𝑘𝑔
𝑡 .5 = [
8 ∗ 0.048 𝑚 𝑠 0.032 𝑚
𝑘𝑔
𝑚
965 𝑚3 9.81 𝑠2 0.000177 𝑚
(− ln (1 −
0.01𝑚
0.01𝑚
)−
)] = 1.61 𝑠 .5
0.032𝑚
0.032𝑚
Equivalent wicking radii
𝑟=
8𝜇𝑋
𝑥
𝑥
(− ln (1 − ) − )
𝜌𝑔𝑡
𝑋
𝑋
𝑘𝑔
𝑟=[
8 ∗ 0.048 𝑚 𝑠 0.032 𝑚
𝑘𝑔
𝑚
965 𝑚3 9.81 𝑠2 0.6 𝑠
(− ln (1 −
0.01𝑚
0.01𝑚
)−
)] = 0.1 𝑐𝑚
0.032𝑚
0.032𝑚
This was done for all times and distances recorded, the final radii found are averages.
Discussion
Questions:
1) The deviations that occurred from observed capillary flow and theory are likely to have
resulted from experimental error in timing the fluid movement. The largest deviations
occurred when the capillary tubes are parallel to the lab table. This is likely due to the
fact that it is harder to time the fluid in this configuration, especially when considering
the first several points. Secondly the contact of the capillary tube with the fluid
meniscus may have been partial, which would cause dampened wicking at least initially.
2) In order to find the tortuosity of the different wicking papers, it is important to keep the
different fluid types in mind, as the equivalent radii depend greatly on the fluid
properties. Table 4 is expanded below to evaluate the tortuosity of the pore channels. In
order to do so, the actual pore radius must be acquired, and this is roughly discernable
in Figures 6 and 7 as shown in the results. The pore radius of nitrocellulose is
approximately 2.5 micrometers, and that for whatman 41 is found to be approximately
5 micrometers.
𝜏 = 𝑡𝑜𝑟𝑡𝑢𝑜𝑠𝑖𝑡𝑦 =
𝑝𝑜𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠
𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑟𝑎𝑑𝑖𝑢𝑠
[Berg]
As is visible from Table 6, the tortuosity of silicon oil is less than that of de-ionized water
by two or three orders of magnitude, depending on the paper used. This implies that
while the pore sizing and regularity affect how well a fluid wicks into a material, the fluid
properties actually have a greater effect on how well that fluid wets or wicks a given
material.
Table 6: Evaluation of tortuosity of nitrocellulose and whatman 41
Nitrocellulose paper
Whatman 41 paper
Equivalent radii
Tortuosity
Equivalent radii
tortuosity
D.I. Water
0.53 µm
4.72
2.4 µm
2.08
Silicon Oil
0.44 mm
0.00568
0.22 mm
0.0227
3) The differences of the equivalent radii for silicon oil and de-ionized water vary greatly
for both nitrocellulose and whatman 41 papers. There are several possible reasons that
account for this occurrence in the data. Silicon oil and water have a similar volatility
[Berg], which means that the oil wicking experiment should have been covered with a
damp Chem-Wipe as the water wicking experiment was. It is likely that the error
generated by this mistake is not large enough to account for the deviation seen in Table
6 for the effective radii calculated when either de-ionized water or silicon oil was used.
Since the actual pore radius of the filter paper is constant it is the fluid that changes in
how it interacts with the paper. Since the Washburn equation is calculating different
effective radii for each fluid there must be a fluid property that is not accounted for by
the Washburn equation. There may be an interaction that occurs between one of the
fluids and the filter paper that does not occur for the other fluid. This would potentially
explain the difference observed in the data.
4) Heat pipes utilize wicking to carry a fluid from a condenser to a source of heat. The heat
causes evaporation of the fluid, which is carried by either diffusion or pumped towards
the condenser. The heat pipe makes use of the latent change of heat between the
liquid and gas phase when removing heat from the heat source. The advantages to the
heat pipe are that they are cheap and effective. The disadvantages to using a heat pipe
are the size limitations and that the operating temperature greatly affects the efficiency
of the wicking material and fluid. This second reason is a disadvantage if the operating
temperature were to change, because the fluid or wicking material may have to change
as well.
Sources of Error
The largest sources of error in this experiment were due to human reflex and coordination. The
experiments occurred in a rapid fashion, and our group experienced difficulty starting the time
at the exact moment that the wicking paper touched the fluid. This was also a difficulty with the
capillary tubing. When the capillary tube was parallel to the meniscus, it was difficult to identify
the meniscus within the capillary tube until the fluid had traveled 1-3 cm. Error appears to be
the most significant in the experiment with Ethylene Glycol in the 10 µL capillary tube (Figure
2). This is also visible when de-ionized water is used to wick a flow assay, (Figure 13). The initial
timing is off by several seconds in most trials as demonstrated by the fact that the experimental
data does not show wicking to be zero before the experiment occurs. In another words, on all
of the plots that use wicking or capillary flow, the data should pass through the origin.
An error in experimental setup arose in the wicking portion of the experiment. When deionized water was used, the top of the test tube containing the fluid and the wick was covered
with damp paper due to the volatility of the water. Accordingly, this should have been
performed for the silicon oil as well, as the literature sates that water and silicon oil both have
similar volatilities [Berg].
Analysis of Results
Capillary action in capillary tubes fit the Washburn equation as demonstrated in Figures 2, 3, 4
& 5. In Figure 2 the experimental data parallels the Washburn equation, but it is also shifted
downward from what is expected. This is believed to occur due to experimental error in timing
the motion of the fluid. In Figure 3 there is a lot of overlap between the values predicted from
theory and from the experimental values. One issue encountered in Figure 3 & 5 is that the
value of X was unknown. The equilibrium rise height is known for when the capillary is
perpendicular to the ground, but not when it is at another incline angle. To resolve this issue, a
value of X was chosen that was less than 2 cm greater than the largest distance traveled by the
fluid in a particular capillary at the specified incline. From figure 2, 4 & 5 the experimental
values for a capillary parallel to the ground are seen to deviate from the Washburn predicted
values. This is likely due to experimental error caused by difficulty in timing the initial distance
traveled by the fluid, or by the fact that the capillary might have been at a slight and
unrecorded incline.
The literature states that fluid movement in filter paper is well described by the Washburn
Equation [Berg], but the results from this experiment disagree. Wicking flow experimental
values are compared to the theoretical values predicted by the Washburn equation in Figures 8,
9, 10 & 11. The data only fits the predicted values in one case, and that is when de-ionized
water wicks into nitrocellulose as is visible in Figure 8. Examination of Table 6 shows that the
tortuosity of whatman 41 and nitrocellulose are of the same order of magnitude for de-ionized
water. It might be expected then that de-ionized water would wick both papers as predicted by
the Washburn equation. From Figure 9 it can be seen that this is not the case, either due to
experimental error or an effect of the pore size and shape of the whatman 41 paper upon deionized water.
When silicon oil is used instead of water, wicking is not described by the Washburn equation
regardless of the paper used as is demonstrated in Figures 10 & 11. In fact, the wicking of either
paper with silicon oil is better described by a first order dependence on time then by the
Washburn format. It shall be noted here that the experiment performed for silicon oil and
nitrocellulose and the whatman 41 filter paper may end with different results if the test tube
were instead covered by a damp cloth, to prevent evaporative losses from the wick. It is likely
that this error is to blame for the disagreement for the discrepancy between the Washburn
format and the experimental data. This is because of the fact that the wicking values are
consistently less than those predicted by the Washburn equation. If evaporative losses were
prevented, then the rate of wicking would increase. The Washburn equation cannot take into
account the evaporation that occurs during the exercise, and would therefore not be able to
predict the wicking rate of silicon oil observed. The best way to test this would be to perform
the same experiment with wicking paper and silicon oil as performed before, but with the
exception of covering the test tube with a cloth dampened with silicon oil.
The Washburn equation takes surface tension and viscosity into account, which implies that a
different fluid property is responsible for the differences between water and silicon oil when
wetting nitrocellulose. I hypothesize that this difference is due to an interaction that occurs
between the de-ionized water and the nitrocellulose, and that this interaction does not occur
between silicon oil and the nitrocellulose. In all but one case the actual wicking values are lower
than those predicted by the Washburn equation, which means that wicking paper is not as
efficient as a single small capillary, perhaps due to the papers tortuosity. A single capillary is a
straight shot, but a piece of filter paper is a maze of broken capillaries. It therefore may be
expected that filter paper will not wick as well as a small capillary, and this is demonstrated by
the disagreement between Washburn equation and the wicking data in most cases.
The movement of dye across a lateral piece of packed wicking paper is not described by the
Washburn equation, but rather a linear fit. The velocity appears constant and depends only on
a first order relationship to time. This is not the case for the movement of water across the
same wick when the wick is dry. Figure 12 demonstrates the fact that de-ionized water wicks
nitrocellulose paper with a dependence on the square root of time, or in other words in the
Washburn format. This is in agreement with the results in Figure 8. This means that the dye
does not move at a constant velocity because of the wicking paper itself, otherwise the water
would also demonstrate a constant velocity. I hypothesize that the dye’s movement in the
wicking paper would be better described by a counter-diffusion model then the Washburn
equation. This is supported by the fact that the water wicks the paper at different time
dependence then the dye does. If the dye displacement is described by an equal molar counterdiffusion model, then the geometry of the wick will affect the rate of diffusion. This means that
an additional experiment could be performed with a disk cut out of nitrocellulose. It could be
wetted, and then the dye placed into the center of the disk. If the displacement of the dye is a
factor of 2πr (the perimeter of the circle covered by the dye) less than when the experiment is
performed with a straight wick, then it is likely that the diffusion model will describe the
displacement of the dye over time.
Conclusion
From the results of this experiment two things can be concluded. The first is that capillary
action in capillary tubes is generally described by the Washburn equation. The second is that
wicking flow is not generally described by the Washburn equation, but instead depends on the
wicking material structure, and on any interactions that may occur between the fluid and the
wicking material.
References
Berg, J. C. (2010). An Introduction to Interfaces & Colloids: The Bridge to Nanoscience. New
Jersey: World Scientific (pp. 55, 284-289)