Lee Hwa Chung theorem: Difference between revisions
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'''Porosimetry''' is an [[Measurement|analytical technique]] used to determine various quantifiable aspects of a material's [[Porosity|porous]] nature, such as '''pore diameter''', total '''pore volume''', [[surface area]], and [[Bulk density|bulk]] and absolute [[density|densities]]. | |||
The technique involves the intrusion of a [[wetting|non-wetting]] liquid (often [[Mercury (element)|mercury]]) at high [[pressure]] into a material through the use of a '''porosimeter'''. The pore size can be determined based on the external pressure needed to force the liquid into a pore against the opposing force of the liquid's [[surface tension]]. | |||
A force balance equation known as [[Washburn's equation]] for the above material having [[Cylinder (geometry)|cylindrical]] pores is given as:<ref>A.B. Abell, K.L. Willis and D.A. Lange, "Mercury Intrusion Porosimetry and Image Analysis of Cement-Based Materials", Journal of Colloid and Interface Science, 211, pp. 39-44 (1999). [http://faculty.arch.tamu.edu/anichols/index_files/pubs_data/tri-prin97/tri-prin97.htm]</ref> | |||
:<math>P_L - P_G = \frac{4 \sigma \cos \theta}{D_P}</math> | |||
:<math>P_{L}</math> = pressure of liquid | |||
:<math>P_{G}</math> = pressure of gas | |||
:<math>\sigma</math> = surface tension of liquid | |||
:<math>\theta</math> = [[contact angle]] of intrusion liquid | |||
:<math>D_{P}</math> = pore diameter | |||
Since the technique is usually done under [[vacuum]], the gas pressure begins at zero. The [[contact angle]] of [[Mercury (element)|mercury]] with most solids is between 135° and 142°, so an average of 140° can be taken without much error. The [[surface tension]] of mercury at 20 °C under vacuum is 480 [[millinewton|mN]]/[[Metre|m]]. With the various substitutions, the equation becomes: | |||
:<math>D_P = \frac{1470 \ \text{kPa} \cdot \mu \text{m}}{P_L} </math> | |||
As pressure increases, so does the cumulative pore volume. From the cumulative pore volume, one can find the pressure and pore diameter where 50% of the total volume has been added to give the median pore diameter. | |||
==References== | |||
{{reflist}} | |||
[[Category:Measurement]] | |||
[[Category:Scientific techniques]] | |||
[[Category:Porous media]] | |||
Latest revision as of 05:48, 15 March 2013
Porosimetry is an analytical technique used to determine various quantifiable aspects of a material's porous nature, such as pore diameter, total pore volume, surface area, and bulk and absolute densities.
The technique involves the intrusion of a non-wetting liquid (often mercury) at high pressure into a material through the use of a porosimeter. The pore size can be determined based on the external pressure needed to force the liquid into a pore against the opposing force of the liquid's surface tension.
A force balance equation known as Washburn's equation for the above material having cylindrical pores is given as:[1]
- = pressure of liquid
- = pressure of gas
- = surface tension of liquid
- = contact angle of intrusion liquid
- = pore diameter
Since the technique is usually done under vacuum, the gas pressure begins at zero. The contact angle of mercury with most solids is between 135° and 142°, so an average of 140° can be taken without much error. The surface tension of mercury at 20 °C under vacuum is 480 mN/m. With the various substitutions, the equation becomes:
As pressure increases, so does the cumulative pore volume. From the cumulative pore volume, one can find the pressure and pore diameter where 50% of the total volume has been added to give the median pore diameter.
References
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