Thermodynamics and hydrodynamics of spontaneous and forced imbibition in conical capillaries: A theoretical study of conical liquid diode

TL;DR

This paper presents a theoretical analysis demonstrating that conical capillaries can function as liquid diodes, allowing spontaneous and forced imbibition predominantly in one direction based on thermodynamic and hydrodynamic principles.

Contribution

The study derives analytical formulas for critical contact angles and demonstrates how conical capillaries can be designed to act as liquid diodes through thermodynamic and hydrodynamic analysis.

Findings

Conical capillaries can be engineered to act as liquid diodes.

Spontaneous imbibition occurs only in the forward direction under specific contact angles.

The time scale of imbibition favors the forward direction, enhancing diode functionality.

Abstract

Thermodynamics and hydrodynamics of spontaneous and forced imbibition of liquid into conical capillaries are studied to assess the feasibility of a conical liquid diode. The analytical formulas for the Laplace pressure and the critical Young's contact angle of the capillary for the onset of spontaneous imbibition are derived using the classical capillary model of thermodynamics. The critical contact angle below which the spontaneous imbibition can occur belongs to the hydrophilic region for the capillary with a diverging radius while it belongs to the hydrophobic region for the capillary with a converging radius. Thus, by choosing Young's contact angle between these two critical contact angles, only the spontaneous imbibition toward the converging radius occurs. Therefore, the capillary with a converging radius acts as the forward direction and that with a diverging radius as the reverse direction of diode. Even under the external applied pressure, the free-energy landscape implies that the forced imbibition occurs only to the forward direction by tuning the applied pressure. Furthermore, the scaling rule of the time scale of imbibition is derived by assuming Hagen-Poiseuille steady flow. Again, the time scale of the forward direction is advantageous compared to the reverse direction when the imbibition to both direction is possible. Therefore, our theoretical analysis shows that a conical capillary acts as a liquid diode.