Capillary action with respect to "wicking beds"

1. Aug 23, 2014

dferasmus

Good day

I am interested in making a wicking bed for typical vegetable growing. I have read that the height of the soil should be no higher than 300mm. I suspect this number is experimental or simply copied from other sources.

I am a little more curious regarding the mechanics of such a system.

Please follow me on this brief journey and correct me if I divide by zero.

If I where to Engineer It, I would be tempted to look at soil granule size and from that derive an average, and approximate, pore size. From the average pore size I would want to consider capillary action and determine a theoretical height. At that height I would try to determine a possible water pressure and linearly plot it through the height of the soil. On this plot I would mark the field capacity and permanent wilting point, if possible.

A few assumptions;
The soil consists of only one grain size, no organic matter and pure water is used.
Pore size is calculable from the grain size.
Pore size is similar to tube size in capillary action.
Field capacity is about -33kPa and the permanent wilt point is about -1500kPa.

Another assumption would be that all this is theoretical, however feel free to question my sources.

Sand granule size would be determined from available data: Medium Sand - 0.25mm to 0.5mm, with a 38% porosity
"irrigation.wsu.edu/Content/Fact-Sheets/Soil-Monitoring-and-Measurement.pdf" [Broken]

To calculate average pore size: granule size * porosity = pore size * (100% - porosity)
Therefore: pore size = granule size * porosity / (100% - porosity)
For 0.25mm: pore size = 0.25mm * 38 / 62 = 0.15mm
For 0.5mm: pore size = 0.5mm *38 / 62 = 0.31mm

Assume pure water in a clean glass tube for simplicity in calculating capillary action:
capillary height = 2 * surface tension of water / (radius of tube * gravitational acceleration * density of water)
For 0.15mm: capillary height = 2 * 72.75mN/m / (0.15mm / 2 * 9.8m/s/s * 1000kg/m/m/m) = 0.198m
For 0.31mm: capillary height = 2 * 72.75mN/m / (0.31mm / 2 * 9.8m/s/s * 1000kg/m/m/m) = 0.096m

water pressure = -density of water * gravitational acceleration * height
For 0.198m: water pressure = -1000kg/m/m/m * 9.8m/s/s * 0.198m = -1.94kPa
For 0.096m: water pressure = -1000kg/m/m/m * 9.8m/s/s * 0.096m = -0.94kPa

I have read field capacity could be -10kPa for sand, but I suspect it depends on the water retention curve.

For this thought experiment the sand is below a field capacity of -33kPa (And -10kPa) and for a field capacity of -33kPa a height of 3.3m (And -10kPa from a height of 1m) is required. This would suggest that there is more water than air which is less than optimal (Dependent on water retention curve).

It would also suggest that sand is not useable to 300mm.

Lets see what results sandy loam gives with the following specs;
Sand at 60% with a granule size of 0.175mm.
Silt at 30% with a granule size of 0.020mm.
Clay at 10% with a granule size of 0.002mm.

The average granule size would be:
average granule size = sand granule size * sand percentage + silt granule size * silt percentage + clay granule size * clay percentage
average granule size = 0.175mm * 60% + 0.020mm * 30% + 0.002mm * 10%
average granule size = 0.111mm

The porosity of sandy loam is 43%.
"irrigation.wsu.edu/Content/Fact-Sheets/Soil-Monitoring-and-Measurement.pdf" [Broken]

The pore size is therefore 0.084mm (See above equations).

The capillary height is therefore 0.354m (See above equations).

At this height water pressure is -3.47kPa (See above equations).

Water pressure at -1kPa occurs at 0.102m.

Funny how the equations suggest what is taken at face value; 300mm height.

What Im lacking is a representation of water pressure vs water content for specific soils (Water retention curves) so that I could determine at what height the soil experiences its field capacity (Which appears to be soil parameter dependent); at which pressure water content becomes less that at saturation (Air starts getting to the roots).

Have I befouled physics and / or can any one give me some more info, especially regarding water retention curves (Theoretical).

Thanks
dferasmus

Last edited by a moderator: May 6, 2017
2. Aug 28, 2014

Greg Bernhardt

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

3. Aug 29, 2014

dferasmus

Greg

No worries, I tend to ask very specific questions. Thanks for the timeout reply I at least know it gets attention.

I do have further information though; It appears (Im teaching myself) that the capillary method I used is a good approximation for an ideal setup and does not include the water retention curve. I had thought that from the capillary data I could deduce the water retention curves, instead its an alternative.

I did find some interesting information by Fredlund et al.;

They analysed many soil types and generated an appoximation of the water retention curve with soil grain size as the independent variable. Very interesting stuff.

HOWEVER! In trying to recreate the equations, for confirmation, before blindly using them and I have found a discrepency in the equations to detemine nf and mf and the curve fitting parameters.

Firstly the crossover appears to occur at an effective grain size diameter 100 times smaller than the paper. This is a comparison between the graphs and the recreated equaton in the paper. I have simply compensated by dividing the effective diameter by 100.

Secondly the clay (0.0001 effective diameter) appears, and is suggested, to result in an nf of 1 and mf of 0.5, however the equations I have recreated only approach these values. I cannot reporoduce the clay curve of Fig 4.

These two discepencies bother me, but, as the work in a whole is an approximation anyway, I think its good enough for what I want

I have tried to attach an excel spreadsheet if anyone would like to confirm my "code".

Thanks
dferasmus

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