Furmidge Equation Revisited.

Area of Science:

• Interfacial Science
• Fluid Dynamics
• Surface Chemistry

Background:

• The Furmidge equation models forces on sliding drops, but relies on a discontinuous contact line assumption.
• Experimental data shows a wide range of the geometrical prefactor (k), lacking a clear physical explanation.
• Existing corrections introduce derivative discontinuities, limiting the model's applicability.

Purpose of the Study:

• To address the limitations of the Furmidge equation by developing a more general model for the contact line force.
• To provide a physical explanation for the experimentally observed range of the geometrical prefactor (k).
• To accurately model the contact angle's behavior at the contact line.

Main Methods:

• Developed a general model for contact line force using a Fourier series.
• Further generalized the model by superposing Gaussian curves onto the Fourier series.
• Fitted the derived functional form for the contact angle to experimental data.

Main Results:

• The generalized model successfully predicts a range of geometrical prefactor (k) values consistent with experimental findings.
• The model's functional form for the contact angle shows good agreement with experimental data.
• The study establishes good agreement between the model's predicted and experimental k values.

Conclusions:

• The developed model offers a more robust framework for understanding forces on sliding drops.
• The study provides a physical basis for the variability of the geometrical prefactor (k).
• The findings improve the accuracy of interfacial force calculations in fluid dynamics.