modelling and experimental investigation of paint mixing process dynamics

Abstract

In most paint mixing machines, users usually depend on visual observation of the paint mixture or they may specify a preset time for stirring chosen based on previous experience to ensure the homogeneity of the paint, but this period may be not sufficient to satisfy a perfect homogeneity of the paint mixture. So, such a practice may lead to inconsistency in paint quality. In this work, an automatic paint mixing machine that is equipped with a monitoring and control system has been designed and constructed. This machine aims to mix and analyze the desired paint color. Arduino Mega was used as micro-controller and a high-resolution camera was used for paint image capturing. A mixing algorithm for water-based paints was proposed. This algorithm guarantees a user to obtain a predefined paint color within a specific time. That means, the user determines the paint volume and color as inputs to the algorithm. Then, based on paints commercial database, the algorithm will specify the needed amount from the three basic colors (red, green and blue paints) to be mixed. Experimental investigation of the effects of process parameters of the designed conventional mixing vessel has been implemented through measuring the time-varying color state of the paint mixture. The independent variables include the stirring speed, the tristimulus value of the desired paint color and the batch volume. The dependent variable is the color distance, which represents the range between the mixed and the unmixed paint color. The independent variables are manipulated separately, while reporting the values of the dependent variable with time. Three empirical models were proposed including the solution for first, second and complex second order differential equations. Then, the obtained color distance function was fitted to the empirical models in order to choose the best fit model, based on minimizing the objective function using least square method implemented as an algorithm in the Matlab framework. The solution for complex second order differential equation provides the best fit for the observed dynamic curves. It is concluded that the speed of convergence to steady state increases with increasing stirring speed and decreasing batch volume. However, changing the tristimulus value of the desired paint color has no major effect of the speed of convergence to steady state, while it only changes the steady state distance of the desired paint color. Furthermore, the developed paint mixing machine can be used for experimental investigation of kinetic studies of various industrial and environmental reactive processes.