Multi-objective optimization of the magnetic wiping process in dip-coating

TL;DR

This paper develops a multi-objective optimization framework for electromagnetic wiping in dip-coating, balancing efficiency, smoothness, and heating, using a 1D model to identify optimal conditions and analyze effects of magnetic field parameters.

Contribution

It introduces a multi-gradient optimization method for electromagnetic wiping, providing insights into how magnetic field parameters influence performance and energy consumption.

Findings

Wiping efficiency depends only on Hartmann number (Ha).

Liquid thickness becomes insensitive to magnetic field intensity beyond a threshold.

Joule heating is mildly affected by magnetic field shape and strength.

Abstract

Electromagnetic wiping systems allow to pre-meter the coating thickness of the liquid metal on a moving substrate. These systems have the potential to provide a more uniform coating and significantly higher production rates compared to pneumatic wiping, but they require substantially larger amounts of energy. This work presents a multi-objective optimization accounting for (1) maximal wiping efficiency (2) maximal smoothness of the wiping meniscus, and (3) minimal Joule heating. We present the Pareto front, identifying the best wiping conditions given a set of weights for the three competing objectives. The optimization was based on a 1D steady-state integral model, whose prediction scales according to the Hartmann number (Ha). The optimization uses a multi-gradient approach, with gradients computed with a combination of finite differences and variational methods. The results show that the wiping efficiency depends solely on Ha and not the magnetic field distribution. Moreover, we show that the liquid thickness becomes insensitive to the intensity of the magnetic field above a certain threshold and that the current distribution (hence the Joule heating) is mildly affected by the magnetic field's intensity and shape.