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Nonlinear effects due to gravity in a conical Hele-Shaw cell
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil. jme@lftc.ufpe.br
Summary
Gravity and conical cell geometry significantly alter viscous fingering patterns. Finger tip splitting and competition dynamics change based on fluid properties and cell angle, revealing complex pattern evolution.
Area of Science:
- Fluid Dynamics
- Pattern Formation
- Nonlinear Dynamics
Background:
- Viscous fingering is a classic instability in fluid dynamics.
- Hele-Shaw cells are model systems for studying fluid interfaces.
- Gravity's role in such instabilities is often complex and nonlinear.
Purpose of the Study:
- Investigate viscous fingering in a conical Hele-Shaw cell with gravity.
- Analyze the combined effects of gravity and cell topology on pattern evolution.
- Understand gravity-induced nonlinear effects on fingering dynamics.
Main Methods:
- Utilized a conical Hele-Shaw cell setup.
- Employed a mode-coupling approach to study gravity-induced nonlinear effects.
- Varied cell opening angle and fluid properties (density, viscosity).
Main Results:
- The interplay of gravity and cell topology profoundly modifies fingering patterns.
- Finger tip splitting intensity depends on cell opening angle and fluid properties.
- Finger tip splitting can be replaced by sharpening with varying cell angles.
- Finger competition dynamics are enhanced or restrained by fluid density.
Conclusions:
- Gravity and conical geometry introduce significant nonlinear effects in viscous fingering.
- Cell topology and fluid properties dictate finger tip morphology and competition.
- The study provides insights into complex pattern evolution in confined geometries under external forces.