Viscous entrainment from a nozzle: singular liquid spouts.

Area of Science:

• Fluid Dynamics
• Rheology
• Continuum Mechanics

Background:

• Viscous entrainment describes fluid being drawn into a flow.
• Understanding entrainment transitions is crucial for predicting fluid behavior in nozzles.
• Previous models often simplified the complex dynamics near the entrainment threshold.

Purpose of the Study:

• To investigate the nature of viscous entrainment transitions from a nozzle.
• To determine if continuous transitions are possible under specific conditions.
• To characterize the morphology of the entrained fluid at the transition point.

Main Methods:

• Analysis of a long-wavelength model for viscous entrainment.
• Imposition of specific large-scale boundary conditions.
• Mathematical characterization of the steady-state entrained flow.

Main Results:

• Demonstrated that viscous entrainment transitions can be continuous.
• Observed that the entrained steady-state spout becomes vanishingly thin near the threshold.
• Characterized the spout as a thin tendril emerging from a conical base profile.

Conclusions:

• Continuous entrainment transitions are achievable in viscous flows from nozzles.
• The geometry of the entrained fluid exhibits a distinct thin tendril morphology at the threshold.
• The findings offer insights into fluid behavior under specific boundary conditions.