Thermal Marangoni instability and magnetic pressure for a thin ferrofluid layer

Area of Science:

• Fluid dynamics
• Magnetohydrodynamics
• Instability phenomena

Background:

• Ferrofluids exhibit complex behaviors under external fields.
• Marangoni and Cowley-Rosensweig instabilities are crucial in fluid systems.
• Understanding coupled instabilities is vital for predicting fluid behavior.

Purpose of the Study:

• To investigate the linear coupling between Marangoni and Cowley-Rosensweig instabilities.
• To analyze the effect of magnetic fields and temperature gradients on ferrofluid layers.
• To determine how these factors influence instability onset and patterns.

Main Methods:

• Linear stability analysis.
• Consideration of a thin ferrofluid layer with a rigid plate and a free surface.
• Analysis of stationary and oscillatory cases with varying heating directions and magnetic field strengths.

Main Results:

• A magnetic field, below the critical Cowley-Rosensweig value, significantly reduces the critical Marangoni number.
• A new instability pattern emerges for specific dimensionless wavenumbers.
• Heating from the gaseous phase theoretically allows for an oscillatory marginal case under unphysical conditions.
• The critical Rayleigh-Taylor instability wavelength is affected when the ferrofluid hangs from the rigid side.

Conclusions:

• Magnetic fields can drastically alter the onset and nature of instabilities in ferrofluids.
• The interplay between thermal gradients and magnetic fields is key to controlling ferrofluid behavior.
• The findings have implications for microfluidics and heat transfer applications involving ferrofluids.