Journal of the Society of Motion Picture and Television Engineers (1950-1954)

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costly. As long as the desired results are gained, attention is given to expense in only a secondary way. Because the main object is to produce film meeting quality standards, and because silver recovery provides substantial returns, expenditures for raw materials are regarded as of minor importance. Consequently, a replenishment system which consumes tremendous quantities of chemicals and requires extensive control testing is considered, nevertheless, successful as long as film which satisfies quality requirements is produced. In an effort to deal with the problem of quality control without resorting to excessive use of chemicals or labor, the problem of replenishment is approached here by analyzing the process in terms of the basic factors involved. Chemicals lost from processing solutions as film is processed must be replaced by the replenishers at the same rate at which they are lost. Similarly, those gained during processing must concurrently be eliminated, through the action of the replenishers. Carryover of liquid by the film, and reaction between film and solution chemicals, cause the main changes in composition of the processing solutions. If rates of carry-over and reaction in a system are known, then it is a simple matter to calculate the replenishment that a system demands. These rates cannot always be measured directly, but equations can be formulated which express them in terms of measurable quantities. The first portion of this paper deals with the methods of determining rates of carry-over and reaction, while the latter portion shows how these values may be applied in calculating replenishment rates and formulas. Determination of Carry-Over Rates When wet leader enters and passes through a solution, the concentration of each chemical in the solution becomes reduced, even though no chemical reactions occur. Water carried in by the leader dilutes the solution, while liquid carried out by the leader withdraws chemicals from the solution. If the symbol W represents quantity of a constituent in a tank, and if/ represents the number of feet of leader entering and leaving the tank, then the derivative dW/df represents the rate of loss of constituent from the tank. A constituent removed from a tank by carry-over is lost at a rate equal to the product of the rate of loss of liquid from the tank (B) and the concentration of the constituent at that particular time. It is possible to express concentration in terms of quantity of constituent (W} and volume of liquid in the tank. How much liquid is present in a tank after / ft of leader have passed through it? This volume is determined by the volume of liquid in the tank initially (T), the carry-over of liquid into the tank (Af), and the loss of liquid from the tank by carry-over at the exit (Bf}. When concentration is expressed by the equivalent term, the following differential equation5 may be set up to describe the rate of loss of a constituent from a tank as a result of carry-over: dW -W (A B}f (1) Equation 1 may be solved in the following way5: -Bdf dW w w (A -B)f (2) ~B w r T -\ LL_ — _ _ _ W0 \_T + (A 5JJU -£ = r T T Co LT+(A-B)f_\ Although a complex relationship, involving an exponential term, exists between carry-over and concentration, Goldwasser: Mathematical Replenishment Techniques 13