Mathematical modelling of drying of paint and coatings

NWO has awarded funding of 760,000 euros for research into the mathematical modelling of thin polymer films. In the PRONTO project, mathematicians at Utrecht University and computational chemists at the University of Amsterdam will work together with non-academic partners to develop a new generation of models for materials science. Such models are expected to stimulate progress in a variety of technology areas, from improving the quality of high-speed printing to better understanding of mechanisms behind aging of historic masterpieces. 

The project started from the collaboration between mathematician Ivan Kryven (UU), computational chemist David Dubbeldam (UvA), and chemical engineer Piet Iedema (UvA). Industrial partners include Canon Production Printing, AkzoNobel Performance Coatings, Reden, and the Rijksmuseum. Including the contribution from industry, the total project budget is just over a million euros.

Discover new mathematics

Kryven is very excited about the project. “The Mathematical Institute has a long history of collaborating with industry. We discuss, consult, jointly supervise thesis, and regularly involve industry partners in the study curriculum", he says. "Whenever a mathematical question comes in from industry, we can usually point toward the direction to the solution straight away in about ninety percent of the time. In nine percent of the time, it’s a clear dead end. We know that the question cannot be answered. But in the remaining one percent, which is the case for this project, it becomes very intriguing. The question is neither possible nor impossible to answer with current mathematics. This lends an opportunity to discover new mathematical ideas and expand the horizons of our knowledge. Hence, a great challenge.” 

However thin, they are full of whim

Paints or coating solutions that dry, result in polymer films. Although they look thin and flat, their cross sections contain a complex network of particles resulting in a three-dimensional structure. Kryven is known for modelling such networks, and how they are folded in geometrically. Dubbeldam studies the physical chemistry of the constitute particles, and Iedema the properties of the overall material. “So, we really need each other." Kryven adds: "It reminds me of an old story about blind men and an elephant. They do not know what an elephant looks like, and to learn, they each touch a different part of the animal. Consequently, every man has a limited sense of what the elephant looks like as a whole, and they need to combine each other’s knowledge.”

Society, science, and technology all greatly benefit from the scrupulous but invisible work of mathematicians. However, there is a time lag in the knowledge transfer

As simple as possible, but not simpler

In this project, researchers will approach the problem from two scientific angles simultaneously. They will conduct ‘physical’ experiments with computer simulations, and at the same time build theoretical models. Both lines of research will result in knowledge about film formation. However, knowledge that comes from computer simulations, even from the most powerful supercomputers, can only describe a very limited sized sample of the film, whereas knowledge that springs from mathematical modelling can be applied on an arbitrary large scale. “From the mathematical perspective, the goal is to keep it simple. We will be capturing the essence, looking for the fundamental principles of the process”, Kryven explains. “The benefit is that these models will be applicable to real-size cases of film formation.”  

Narrowing the lag

The results of this project could be applied, for instance, in industrial printing, the development of paint resins, and the field of art restoration and conservation. To Kryven, it is a great example of cooperation between scientific disciplines. “Society, science, and technology all greatly benefit from the scrupulous but invisible work of mathematicians. However, there is a time lag in the knowledge transfer: the mathematical ideas that engineers are putting into practice today were developed several decades ago. It just takes a long time to learn what mathematics has to offer and how to use it“, he says. “It is therefore important that we maintain a good dialogue between the two fields of research, and this is precisely what is happening here.”