Kawakita's experimental equation has been introduced from the relationship observed between pressure and volume in the case of piston compression.
Although the cheracteristic constants a and b in Kawakita's eq. can be obtained by a graphical method, any clear relationship between these constants and physical properties has not been found out.
The authors have carried out an experimental work on the hydrostatic compaction using several kinds of powders, i.e. electrolytic copper, electrolytic iron, reduced iron, atomized iron, molybdenum and tungsten.
From the data obtained, it is found out that the constant a in Kawakita's eq. is nearly equal to the value of volume reducticn at infinitely large pressure, that is the initial porosity.
On all the powders tested, two stages are recognized of the curve of Pb (V-V_∞)/(V_ao-V_∞) versus (V_ao-V)/(V_ao-V_∞), where P is the compacting pressure, b the constant, V-V_∞ the volume of residual porosity, V_ao-V_∞ the volume of initial porosity and V_ao-V the volume of reduced porosity.
In the first stage that is the linear part of the curve, the constant b has a constant value. In this region, the constant b appears to be related with the yield strength σ₀ of the powder particles and apparent initial porosity N_ao.
In the secondary stage that is the curved portion of the figure (Fig. 3), the constant b has not a constant value. In this region, the constant b appears to be related with σ₀*, N_ao and (V_ao-V)/(V_ao-V_∞).
The relationship between σ_t/P and 1/b has a clear linearity, and then this fact means that the constant b is related indirectly to the strength of powder particles.

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Several qnantitative experiments were carried out on the filtration of fine particles of polystylene in dilute suspension using various glass-fiber paper filters. Each experimental run was performed at constant filtration rate by forcing the suspension through the filter using a syringe-type micro-injection pump. From the experiments, the following results were obtained within the range of experimental conditions.
1) The so called log-penetration law is applicable to the thickness of paper filters. The basic equation for filtration could be expressed as eq. (3).
2) The collection efficiency of a single fiber with the interference effect is given by eq. (13). The effect of direct interception seems to be the predominant mechanism for the collection of fine particles in dilute suspension in pure water by the glass fibers.
Further studies are necessary on the effect of both the fibrous solid fraction in a paper filter and electrostatic forces on the collection efficiency in order to elucidate the proportionality constant in eq. (13).

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