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

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 spo...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 34; no. 4
Main Author Iwamatsu, Masao
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.04.2022
Subjects
Blood vessels
Capillaries
Capillary pressure
Contact angle
Contact pressure
Convergence
External pressure
Fluid dynamics
Fluid mechanics
Free energy
Hydrodynamics
Imbibition
Physics
Steady flow
Thermodynamics
Time
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Summary: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 directions is possible. Therefore, our theoretical analysis shows that a conical capillary acts as a liquid diode.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0085412