Analytical approach for the Lucas-Washburn equation

Area of Science:

• Physics of porous media
• Fluid dynamics in confined geometries
• Surface science

Background:

• Porous media characterization often involves studying liquid kinetics.
• Modeling porous media as capillaries faces challenges in estimating pore radius and contact angles.
• The classical Lucas-Washburn equation (LWE) is a key model.

Purpose of the Study:

• To propose an alternative analytical approach to the Lucas-Washburn equation.
• To circumvent difficulties in estimating capillary radius and contact angle.
• To incorporate dynamic contact angles and frictional dissipation into liquid rise models.

Main Methods:

• Analytical modification of the classical Lucas-Washburn equation.
• Modeling capillary rise with a dynamic contact angle.
• Investigating frictional dissipation at the moving wetting front.

Main Results:

• Developed an analytical approach that bypasses direct estimation of capillary radius and contact angle.
• Introduced the concept of a dynamic contact angle for moving liquid fronts.
• Identified frictional dissipation at the wetting front as the cause of time dependence.

Conclusions:

• The proposed analytical method offers a simplified approach to porous media characterization.
• Dynamic contact angles are crucial for accurately modeling liquid kinetics in porous media.
• Understanding frictional dissipation enhances the predictive power of capillary rise models.