Numerical simulation of an off-centered fluid drop in a rotating Hele-Shaw cell

Area of Science:

• Fluid dynamics
• Interface phenomena
• Pattern formation

Background:

• Standard rotating Hele-Shaw cell flows exhibit intricate interfacial patterns due to centrifugal and surface tension forces.
• In these flows, fingers of an outer fluid penetrate an inner fluid drop centered on the rotation axis.

Purpose of the Study:

• To investigate the effect of an off-centered initial drop position on the dynamics of fluid interfaces in a rotating Hele-Shaw cell.
• To analyze the resulting interfacial pattern morphology and the competition among penetrating fingers.

Main Methods:

• Numerical simulations utilizing the level set method.
• Exploration of the off-centered situation with varying distances (d) from the rotation axis.

Main Results:

• The off-center parameter (d) critically influences finger morphology and dynamics at nonlinear stages.
• Asymmetric interfacial patterns emerge and drift away from the rotation axis.
• The effective surface tension parameter (B) impacts the behavior of these centrifugally driven patterns.

Conclusions:

• Off-centering a fluid drop introduces significant asymmetry into centrifugally driven interfacial instabilities.
• The study reveals novel pattern dynamics and transport phenomena in rotating Hele-Shaw cells with off-centered configurations.