Motion Planning for Viscous Fingering

This letter considers the problem of controlling the shape of the moving interface between two fluids contained in a Hele-Shaw cell during its filling. This system is subject to viscous fingering. The interface shape dynamics is described using a modal decomposition where each mode is governed by a...

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Bibliographic Details
Published inIEEE control systems letters Vol. 8; pp. 1409 - 1414
Main Author Petit, Nicolas
Format Journal Article
LanguageEnglish
Published IEEE 2024
Subjects
Automatic Control Engineering
Computer Science
control of micro- and nano-systems
distributed parameters systems
Dynamics
Fingers
Fluids
Hele-Shaw cell
Mathematical models
Microfluidics
motion planning
non-smooth dynamics
Planning
Shape
Viscosity
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Summary:This letter considers the problem of controlling the shape of the moving interface between two fluids contained in a Hele-Shaw cell during its filling. This system is subject to viscous fingering. The interface shape dynamics is described using a modal decomposition where each mode is governed by a non-smooth ordinary differential equation with a random initial condition that is unknown. Once the interface is visibly non circular, a motion planning technique is employed to control the growth of the modes with the goal of approaching a shape of interest. This letter describes the dynamics at stake, studies its reachability property and proposes a constructive method to solve the motion planning problem. Some numerical experiments illustrate the presented methodology.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3411044