Pancake making and surface coating: Optimal control of a gravity-driven liquid film

Type of content
Journal Article
Thesis discipline
Degree name
Publisher
American Physical Society (APS)
Journal Title
Journal ISSN
Volume Title
Language
en
Date
2019
Authors
Boujo E
Sellier M
Abstract

This paper investigates the flow of a solidifying liquid film on a solid surface subject to a complex kinematics, a process relevant to pancake making and surface coating. The flow is modeled using the lubrication approximation, with a gravity force whose magnitude and direction depend on the time-dependent orientation of the surface. Solidification is modeled with a temperature-dependent viscosity. Because the flow eventually ceases as the liquid film becomes very viscous, the key question this study aims to address is: what is the optimal surface kinematics for spreading the liquid layer uniformly? Two methods are proposed to tackle this problem. In the first one, the surface kinematics is assumed a priori to be harmonic and parameterized. The optimal parameters are inferred using the Monte Carlo method. This "brute-force" approach leads to a moderate improvement of the film uniformity compared to the reference case when no motion is imposed to the surface. The second method is formulated as an optimal control problem, constrained by the governing partial differential equation, and solved with an adjoint equation. Key benefits of this method are that no assumption is made on the form of the control, and that significant improvement in thickness uniformity are achieved with a comparatively smaller number of evaluations of the objective function.

Description
Citation
Boujo E, Sellier M (2019). Pancake making and surface coating: Optimal control of a gravity-driven liquid film. Physical Review Fluids. 4(6). 064802-.
Keywords
Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::40 - Engineering::4017 - Mechanical engineering
Fields of Research::40 - Engineering::4012 - Fluid mechanics and thermal engineering
Rights
All rights reserved unless otherwise stated