Spreading, pinching, and coalescence: the Ohnesorge units

Area of Science:

• Fluid Dynamics
• Rheology
• Surface Science

Background:

• Understanding liquid drop behavior (spreading, pinching, coalescence) is vital for applications like spraying, printing, and atomization.
• Existing models based on visco-inertial (VI), visco-capillary (VC), and inertio-capillary (IC) scaling laws lack precise quantitative analysis due to difficulties in estimating parameters.
• Experimental studies often visualize drop dynamics but face challenges in quantitative material characterization.

Purpose of the Study:

• To reanalyze landmark experimental studies on Newtonian fluid drop dynamics.
• To introduce a new framework, "Ohnesorge units," based on intrinsic timescales and lengthscales derived from viscosity, surface tension, and density.
• To demonstrate the universality of drop dynamics across different conditions using this new framework.

Main Methods:

• Reanalysis and summarization of extensive published experimental data on drop spreading, pinching, and coalescence.
• Application of dimensional analysis to identify limiting self-similar cases (VI, VC, IC).
• Development and application of the Ohnesorge units framework, incorporating all three material properties.

Main Results:

• The Ohnesorge units framework, utilizing intrinsic timescales and lengthscales, provides a complementary system to existing scaling laws.
• Analysis of diverse experimental datasets within the Ohnesorge units framework reveals a remarkable collapse of data.
• This collapse highlights shared and universal features in the dynamics of spreading, pinching, and coalescing drops.

Conclusions:

• The Ohnesorge units offer a powerful tool for quantitative analysis and material characterization of drop dynamics.
• This unified approach simplifies the understanding of complex fluid behaviors across a wide range of conditions.
• The findings emphasize the universal principles governing liquid drop interactions in various scientific and industrial applications.