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Volume: 14 | Article ID: art00023_1
Optimization of Ink-Jet Inks Using Nonlinear Programming
Published OnlineJanuary 1998
Abstract

The physical properties of an ink-jet ink such as its absorbance, surface tension and viscosity vary with the concentrations of its components. If each property were only a function of one of the components, formulating an ink to meet a given specification would be straightforward. Unfortunately, just the opposite is usually the case, and the problem becomes a multivariable one in which each property depends on the concentration of more than one of the components. Thus, any one property can be brought into specification by adjusting the concentration of one of the components, but then some of the others can possibly be driven out of specification with the process repeating itself. This can be particularly frustrating when multiple adjustments are being made on a manufacturing batch of ink and time is of the essence.One approach to handling this type of situation is to treat it as a nonlinear programming problem. Each physical property is expressed as an equation in terms of the concentrations of the components that control its value. The data may be regressed using either theoretical relationships or simply empirical ones. The objective function to be minimized is the sum of the deviations that the physical properties are away from their specified centerline values. Alternately, it could be the cost of the ink. The constraints are defined by the upper and lower limits set on the physical properties and that the fractional concentrations must add up to one.Solver, which is an Excel Add-in, was used to solve this set of equations. An example is given that demonstrates how multiple adjustments of a manufacturing batch can be reduced to just a single one via this technique.

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