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The latter term, involving D, obviously disappears for nonreactive constituents. In tanks where the rates of gain and loss of liquid are equal, the quantity of constituent in the replenisher should be:
R =
0 C0A0 + D0
(51)
--B/ TD -Bf
Wr = W0(\ ei ) + ±£ (1 e * )
(49)
Daily replenishment of such solutions as the glycerine stabilizer is often accomplished on the basis of this equation.
New Operating Conditions
A developing machine generally is not operated week after week at the same speed, nor are developing machines expected to process exclusively only one kind of film emulsion, film type or film size. A particular replenishment rate and formula calculated from Eq. (40) constitute optimum values for only one particular machine velocity and film; other conditions require other rates and formulas. It is impractical to change the formulation of the replenisher solution frequently, but if the replenishment rate is adjusted appropriately for each situation, the same replenisher formula may serve satisfactorily for all conditions. Expressions can be readily derived from Eq. (40) to describe the replenishment rate for a new condition, on the basis of the original replenishment rate and the parameters of the original and the new condition:
(1) When machine speed is changed, the new replenishment rate can be calculated from:
R
R0V V0
C0A0 + D —
(50)
The symbols A0, V0 and R0 represent values obtained at the original machine speed. The replenishment rate should evidently vary in about the same proportion as the machine velocity.
(2) When type, or average density, of film is changed, the new replenishment rate should be:
Values of A0 and D0 are obtained from the original film type or film density. The most critical constituent determines the values assigned for Coy D0 and D.
(3) When leader, rather than film, is run through the machine, the replenishment rate should be:
C0A
CoA0 + D
(52)
Here, too, C0 and D are based on the most critical constituent. A tank which receives dry leader would require, according to the above equation, a replenishment rate of zero. No water is brought in by the leader, and solution lost by carry-over at the exit must obviously be replaced. In this special case, replenishment can be accomplished with a solution compounded from the basic — not the replenisher — formula.
Illustration
An example will demonstrate how the replenisher equations can be used in calculating replenisher formulas and rates.
A processing solution is prepared according to the following specification:
X = 60 g/1 Y = 60 g/1 Z = 4.00 g/1
Component X does not react; component Y is consumed at the rate of 15 g/1 000 ft; component Z, which must be held within the narrowest concentration range, is formed at the rate of 10 g/1 000 ft. The carry-in rate is 0.15 gal/1000 ft and the carry-out rate is 0.25 gal/1000 ft. The film travels through the machine at 70 fpm. Solubility of X is 200 g/1; of Y is 140 g/1; and of Z is 10 g/1. What should the replenishment rate and formula be?
Calculations: The minimum value of R is determined:
Goldwasser: Mathematical Replenishment Techniques
21