In percolation, from the instant the stratum of menstruum commences to penetrate the material until it escapes, we have maceration connected with alteration of the position of the mass of the liquid. There are continually new surfaces of contact formed as the liquid passes downward towards the exit of the percolator, and in maceration this phenomenon is also presented. There is no rest within the vessel while solution progresses. Mediums of greater specific gravity than the original menstruum are constantly forming, which, obedient to gravity, seek the lowest portion of the vessel, in turn to be displaced by heavier liquids. In this way, during maceration numbers of percolating currents are flowing throughout the capillaries, and between the interstices of the material, as in percolation, while fresh portions of liquid are continually coming into contact with new surfaces, and saturations are giving way with perfect regularity to those not saturated.
Thus circulation of currents progresses and will continue until an equilibrium is established, as long as there is soluble matter and unsaturated menstruum within the percolator, and afterwards whenever the temperature is permitted to change. Therefore maceration cannot be disconnected from percolation, and as we have seen percolation must include maceration. Thus the contact of maceration and the contact of percolation are identical. Reasoning from the foregoing it may be argued that the expression, maceration in connection with ercola-tion, is simply an expression to imply prolonged contact of liquid with material, by which means we may overcome a defective contact of height of material within the percolator. Upon the other hand, increase of height of powder may imply prolonged maceration of the material with successive portions of menstruum.
We may be justified in arguing that the influences which modify contact are of vital interest in the study of percolation; that the solvent action of a percolating menstruum may be facilitated by judicious maceration, or by increasing the perpendicular height of the powder.
Let us now consider the vessel which contains the material known as the percolator. This is of the utmost importance, as the increase and decrease of diameter governs capacity, subservient to mathematical laws, which it is necessary to examine.
The percolator controls the height of powder under like pressure. As the diameter of the percolator decreases it is responded to by greater, and as it in-creases by less height, both of powder and menstruum. Thus, if a cylindrical percolator be 6 in. in diameter, and a given amount of liquid or powder occupy a height of 6 in., the same material will occupy 13 1/2 in. in height in a percolator 4 in. in diameter; 24 in. in height in a percolator 3 in. in diameter, and 54 in. in height in a percolator 2 in. in diameter.
This is in conformity with the mathematical law that the height of both liquid and powder increases inversely as the square of the diameter of the percolator; a rule, however, which does not apply to the increase and decrease of the resultant contact between the material and passing liquid, as a more careful examination will illustrate.
Let us represent contact by numbers. If a cylindrical or prismatic percolator be used which has been filled 1 in. with a powder, overlying which is alcohol to the depth of 1 in., it is evident that every particle of the powder which assists to form any perpendicular line or column of the powder 1 in. in height will be exposed to and come into contact with every collection of molecules in the line or column of alcohol perpendicular above, providing the alcohol passes directly through the powder from top to bottom. If we knew the number of particles of powder and the number of molecules of alcohol in their respective columns, by multiplying the numbers together the product would represent the individual contacts between particles and molecules. As before remarked, we cannot calculate the number of molecules in a given bulk, therefore we will simply call the inch of alcohol and the inch of powder one, and thus by multiplying one by one we have the product one, which we will take as unity. If the powder be 2 in. in depth and the alcohol be 1, or if the alcohol be 2 in. in depth and the powder 1, the contact will be twice as great (2x1= 2), and may be represented by 2. If both are 2 in. in depth, the contact will be (2 x 2 = 4) twice as great as the last, or 4 times that of the first, and may be represented by 4, and so on.
Let us now take a percolator and apply the foregoing law of increase of contact. For the sake of obtaining even numbers we will consider a square prism instead of a cylinder, as the principle applies alike to either, although in practice cylindrical percolators are employed.
The area of the base of a square prism 16 in. in diameter is 16 X 16 or 256 sq. in. If a powder properly moistened for percolation be placed in it to the depth of 1 in., above which rests 1 in. of alcohol, there will be 256 cub. in. of each layer, and yet being taken as unity when the alcohol has passed through the powder the contact will be 1 x 1 = 1, and thus the contact may only be represented by one. If a square prism 8 in. in diameter be considered, the area of the base will be 64 sq. in. If filled with powder to the depth of 1 in., over which rests 1 in. in depth of alcohol, each layer will contain 64 cub. in. of material, or } the amount required to fill the 16 in. percolator 1 in. in depth. The 8-in. percolator would therefore have to contain 4 in. in depth of each alcohol and powder before the amount (256 cub. in.) could be reached. Thus the contact will be 4 x 4 = 16.
A prism 4 in. in diameter must be filled 16 in. in depth with both alcohol and powder to contain 256 cub. in. of each material. The contact will consequently be 16 X 16 = 256. Thus continuing our calculations, we have the following table which expresses the contact between material and liquid, in each instance the percolator below being 1/2 the diameter of that above: -
Percolator 16 in. in diameter, alcohol and powder each 1 in. deep, contact, 1.
Percolator 8 in. in diameter, alcohol and powder each 4 in. deep, contact, 16.
Percolator 4 in. in diameter, alcohol and powder each 16 in. deep, contact, 256.
Percolator 2 in. in diameter, alcohol and powder each 64 in. deep, contact, 4096.
Percolator 1 in. in diameter, alcohol and powder each 256 in. deep, contact, 65,536.
It will be seen that with the percolator 1 in. in diameter there will be 65,536 times as much contact between alcohol and powder, inch for inch, as in the 16-in. percolator. Thus we find that whereas the height of both liquid and powder increases inversely as the square of the diameter of the percolator, the contact between liquid and powder increases inversely as the fourth power of the diameter of the percolator.
As we follow a line of experiments, the solution or partial solution of one problem brings us face to face with others. Thus we are led onward, and the more thorough our study of the present, the more important we find it to carefully note the future. The utmost caution is necessary in studying nature's laws, lest from insufficient data we hastily generalise. The foregoing argument regarding the laws of contact is undoubtedly as accurate, from a theoretical view, as those of the mathematical increase and decrease of the capacity of the percolator. In practice, however, the advantage derived from increased contact of height between liquid and powder, is not by any means as great as the foregoing calculations indicate. Counteracting agencies overcome to a very great extent the theoretical advantages contact should afford.