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Interface patterns in two-dimensional Stokes flow are explored. Suction-driven interfaces are unstable, with viscosity contrast critically affecting pattern morphology at second order.

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Area of Science:

  • Fluid dynamics
  • Interface phenomena
  • Non-Newtonian fluid mechanics

Background:

  • Investigating the dynamics of interfaces between fluids is crucial for understanding various natural and industrial processes.
  • Two-dimensional Stokes flow provides a simplified yet insightful model for studying low-Reynolds-number fluid behavior.

Purpose of the Study:

  • To analyze the evolution of interfaces between two Newtonian fluids with differing viscosities under suction or injection.
  • To explore interfacial pattern formation in the transitional regime between linear and nonlinear flow dynamics.

Main Methods:

  • Utilizing a second-order mode-coupling theory to examine interfacial morphology.
  • Comparing theoretical predictions with established results from conformal mapping techniques.

Main Results:

  • Linear analysis shows injection-driven interfaces are stable, while suction-driven interfaces are unstable, with instability growth rate independent of viscosity contrast.
  • Second-order analysis reveals viscosity contrast significantly influences interfacial morphology.
  • The theory successfully reproduces near-cusp pattern-forming structures.

Conclusions:

  • Viscosity contrast plays a critical role in determining interfacial pattern morphology beyond the linear regime.
  • The developed mode-coupling theory is valid across all viscosity contrasts and offers insights into complex pattern formation.