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

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 towards 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 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.

Hydrodynamic metamaterials for flow manipulation: Functions and prospects

“…In addition to hydrodynamic cloaking metamaterials, numerous other hydrodynamic metamaterials are not intended for cloaking purposes, such as liquid diodes, [64,65,[65][66][67][68][69] liquid gates, [70][71][72] among other aspects. Since these studies have already been reviewed in the relevant literature, we will not expand too much on them.…”

“…[53][54][55][56][57][58][59][60][61][62][63] Hence, numerous researchers have investigated bionic liquid diodes. [64][65][66][67][68][69] Similar to an electronic diode that can conduct current in the forward direction and block it in the reverse direction, a liquid device that can rectify liquids to flow in a directional manner can be treated as a "liquid diode". It is noteworthy that although traditional mechanical valves can also perform unidirectional transport functions, traditional mechanical valves are relatively bulky compared to liquid diodes.…”

Motion of Droplets in Lyophilic Axially Varying Geometry-Gradient Tubes

“…Gorce et al explored the optimal imbibition of liquids with different curvature tubes. Singh et al and Iwamatsu presented theoretical investigations of liquid imbibition into capillaries with axially varying geometry, and they found that the conical capillary tube can act as a liquid diode. Michielsen et al have done extensive theoretical work on droplet motion on the outer surface of conical tubes from an energetic point of view, and their work also takes into account the effects of the droplet volume, contact angle, and angle of change of the tube on droplet self-transport.…”