  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.
