Marangoni Effect
Surface tension γ decreases with temperature: γ(T) = γ₀ − γ_T · T.
A horizontal temperature gradient ∂T/∂x creates a surface tension gradient that drives flow:
τ = −γ_T · ∂T/∂x (Marangoni stress at the free surface).
The resulting flow velocity at the surface is u_M = −(γ_T ΔT)/(μ) · f(y)
with a parabolic return flow at depth. This recirculating pattern appears in:
• Tears of wine: alcohol evaporation creates solutal Marangoni flow
• Spreading of surfactants on water
• Crystal growth in microgravity (no buoyancy)
• Welding pool dynamics
Hot side (left, red) has lower γ; cold side (right, blue) has higher γ.
Surface flow moves right→left (hot to cold). Arrows show instantaneous velocity field.