Is it possible to predict in detail the process of formation of a solid from a liquid?

Electrorheological fluid was patented in 1947

Electrorheological fluid was patented in 1947

Under the influence of an electric field, it increases its viscosity in a very short time and creates... a solid. This is the main property of the electrorheological fluid. Over the years, it has found a number of applications, but a good theoretical explanation of its creation was missing. Until now. Everything changed thanks to a group from the Faculty of Physics at the Warsaw University of Technology.

Our scientists: a PhD student Michał Łepek, Agata Fronczak, PhD Eng., associate professor of the university and Piotr Fronczak, PhD Eng., associate professor of the university, described the results of their research in the work "Combinatorial solutions to coagulation kernel for linear chains", published in the journal "Physica D: Nonlinear Phenomena"[1].

How do particles clump?

The work carried out by researchers from the Warsaw University of Technology resulted in a theoretical solution to the process of coagulation ("clumping" of particles), in which the formation of so-called linear chains, or groups of particles arranged in chains, takes place. The most known example of such a process is the coagulation of the electrorheological fluid. Due to its unique properties, it belongs to the so-called smart materials.

"In the presence of an electric field, such a fluid is retained in solidified form between the electrodes", explains Michał Łepek — When the electric field is switched off, the system returns to liquid form.

This process can be seen in the following videos:

More than 70 years of waiting

The electrorheological fluid was patented in 1947 by the American scientist Willis Winslow.

"Over the years, he had found a variety of engineering applications, e.g., in brakes, clutches, shock absorbers, hydraulic valves, abrasive polishing and touch displays [2-8]" says Michał Łepek.

Until now, however, there has been a lack of a strict and effective description of the theoretical coagulation process of such a fluid.

"In our work "Combinatorial solutions to coagulation kernel for linear chains", we introduced equations that allowed us to determine the average size distribution of the formed chains at any stage of the particle merging process" — explains Michał Łepek. "These solutions also provide information on the standard deviation from the average distribution (particularly useful for working with real data!). We compared theoretical solutions with the results of numerical simulation and experimental data. We used the results of the experiment, which was the aggregation of polystyrene particles in a mixture of H2O and D2O, i.e. water and deuterium oxide.

Scientists from the Faculty of Physics of the Warsaw University of Technology obtained a very good, unprecedented compliance. That way, as the reviewers also pointed out, more than 70 years after the invention of the electrorheological fluid, a satisfactory theoretical solution to this process was finally achieved.

What does the creation of the so-called linear chains look like under a microscope? This is shown in the video below:

Help for others

"Our work gives a specific statistical description of the particles at any time of coagulation", says Michał Łepek. "This description can be used to better understand the process dynamics and perhaps to improve the efficiency of devices which use electrorheological coagulation (aforementioned brakes, valves, clutches...). It is possible that this description may be useful more broadly in explaining phenomena occurring in nanoparticle suspensions that may be electrically or magnetically active. It cannot be ruled out (but it is already a pure fiction) that in a year, two or fifty someone will discover a process in sociophysics or biology that occurs exactly according to our aggregation scheme — such things happen in science.

The work of our scientists from the Faculty of Physics also has another advantage.

"The final expressions we obtained are (from our point of view) very simple", says Michal Łepek. "You don't need any knowledge in physics, or even theoretical physics, to apply it. Just take the equations, enter what size of the layout and time we are interested in, and the results are there. Every engineer (or non-engineer) can do this on their computer. Especially since we have published on the Internet a programming library, written precisely for the purpose of this work. Therefore, everything is handed on a platter. It’s a novelty. Until now, theoretical studies on coagulation have been a topic undertaken mainly by a narrow group of scientists. I hope that by simplifying the results of the theoretical description, someone from our or another university of technology will be able to use this description for their work."

New research

Now the team of the Warsaw University of Technology wants to investigate whether the developed description of electrorheological coagulation can also be applied to magnetorheological coagulation (that is, the one under the influence of a magnetic field).

"This would be especially interesting, because the conditions for magnetorheological coagulation are much easier to obtain in real application" — points out Michał Łepek. "Magnetorheological fluid can be for example found in shock absorbers of the U.S. Army's vehicles."



[1] M. Łepek, A. Fronczak, P. Fronczak: Physica D: Nonlinear Phenomena 415, 132756 (2021), Combinatorial solutions to coagulation kernel for linear chains.

[2] A.J. Simmonds: IEE Proceedings D 138, 400-404 (1991), Electro-rheological valves in a hydraulic circuit.

[3] G.J. Monkman: Mechatronics 7(1), 27–36 (1997), Exploitation of compressive stress in electrorheological coupling.

[4] M. Seed, G.S. Hobson, R.C. Tozer, A.J. Simmonds: Proc. IASTED Int. Symp. Measurement, Sig. Proc. and Control, Paper No. 105–092–1 (1986), Voltage-controlled Electrorheological brake.

[5] R. Stanway, J.L. Sproston, A.K. El-Wahed: Smart Mater. Struct. 5, 464–482 (1996), Applications of electro-rheological fluids in vibration control: a survey.

[6] W.B. Kim, S.J. Lee, Y.J. Kim, E.S. Lee: International Journal of Machine Tools and Manufacture 43(1), 81-88 (2003), The electromechanical principle of electrorheological fluid-assisted polishing.

[7] Y. Liu, R. Davidson, P. Taylor: Proceedings of SPIE. Smart Structures and Materials 2005: Smart Structures and Integrated Systems 5764, 92–99 (2005), Investigation of the touch sensitivity of ER fluid based tactile display.

[8] G.J. Monkman: Presence: Teleoperators and Virtual Environments 1(2), 219–228 (1992), An Electrorheological Tactile Display.