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Elastic fingering in three dimensions.

Rodolfo Brandão1, Eduardo O Dias1, José A Miranda1

  • 1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil. jme@df.ufpe.br.

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|June 27, 2019
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Summary
This summary is machine-generated.

Elastic fingering, a pattern formation driven by elastic forces at fluid interfaces, is explored in 3D porous media. A new method minimizes interfacial perturbation growth for better control.

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Area of Science:

  • Fluid Dynamics
  • Pattern Formation
  • Rheology

Background:

  • Elastic fingering, a phenomenon observed in quasi-two-dimensional (2D) fluid flows, arises from elastic gel formation at fluid interfaces.
  • This process involves a complex interplay between viscous and elastic forces, leading to distinct pattern morphologies compared to purely hydrodynamic viscous fingering.

Purpose of the Study:

  • To investigate the occurrence and characteristics of elastic fingering in radial fluid displacements within a 3D uniform porous medium.
  • To analyze the influence of combined viscous and elastic effects on interfacial stability and nonlinear pattern formation in this 3D environment.

Main Methods:

  • A perturbative third-order mode-coupling approach was utilized to study linear stability and weakly nonlinear pattern formation.
  • A variational method was employed to develop a time-dependent injection rate scheme for minimizing interfacial perturbation growth.

Main Results:

  • The study examines how viscous and elastic forces jointly affect interface stability and pattern development in a 3D porous medium.
  • A method for controlling pattern growth by adjusting injection rates was determined.

Conclusions:

  • Elastic fingering can occur in 3D porous media, exhibiting unique patterns influenced by both viscous and elastic forces.
  • Controlling interfacial perturbation growth through optimized injection rates is feasible, offering potential for managing pattern formation in such systems.