Physics of Dynamic Contact Line: Hydrodynamics Theory versus Molecular Kinetic Theory
Abstract
1. Introduction
2. Applications of the Dynamic Contact Line
2.1. Coating and Printing
2.2. Healthcare
3. Molecular Kinetic Theory
4. Hydrodynamics Theory
5. Molecular Kinetic Theory: Advantages and Limitations
6. Hydrodynamics Theory: Advantages and Limitations
7. Future Perspectives
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Model | Equation | Condition(s) | Reference |
---|---|---|---|
Hoffman | Experimental study; forced motion of silicone oil on a glass capillary; applicable for nonvolatile liquids with zero static contact angle; negligible inertia and gravity; flow with low capillary number | [106] | |
Tanner | ; | Experimental study and scaling analysis of spontaneous motion of a viscous liquid droplet on a horizontal substrate; steady-state flow; proportionality constant depends on physical characteristics of liquids and flow; based on lubrication assumption; is the time-varying droplet radius of the droplet and is the time-varying dynamic contact angle; suitable for small dynamic contact angles | [107] |
Hoffman–Voinov–Tanner | Dynamics of contact line motion at low capillary numbers on a substrate with zero static contact angle; microscopic region of the flow is excluded; also suitable for flow with finite (non-zero) static contact angle; derived by numerical, experimental, and theoretical studies; also applicable for physics of viscous evaporative droplet spreading on a substrate | [71,106,107,147,148,149,150,151,152] | |
Generalized Hoffman–Voinov–Tanner | Generalized hydrodynamics theory by Hoffman study; considers non-zero static contact angle; proportionality constant depends on physical characteristics of liquid | [71,106,107] | |
de Gennes | Experimental/theoretical work on liquid movement on a smooth substrate; non-zero finite static contact angle; similar to generalized “Hoffman-Voinov-Tanner” model; slip length is the length of microscopic part of the dynamic contact line in which slip condition is valid; lubrication assumption is applied in the analysis; describes the physics of dynamic contact line for flow at low capillary numbers in the mesoscopic region | [72] | |
Cox | ; ; ; denotes the shear viscosity ratio; positive sign is for advancing dynamic contact line; and negative sign is for receding dynamic contact line | Theoretical analysis; applies slip condition to resolve stress singularity at the dynamic contact line; slip length is the length of microscopic part of the dynamic contact line in which slip condition is valid | [69,108] |
Combined hydrodynamics–molecular kinetic | : positive sign stands for advancing dynamic contact line, and negative sign presents receding dynamic contact line : is Young’s static contact angle for stationary condition; positive sign is for receding liquid motion, and negative sign denotes advancing flow ; is the time-varying droplet radius, and denotes transient dynamic contact angle in the case of droplet spreading on a substrate | Modified hydrodynamics theory proposed by Voinov (1976) with contact line velocity-dependent static contact angle in which static contact angle is defined by molecular kinetic theory proposed by Blake et al. (1969) and Blake et al. (1993); three parameters need to be adjusted to describe the physics of dynamic contact line: λ, κ0, and Ls the combined model is only valid for slow dynamic contact line; not an appropriate model for describing the physics of dynamic contact line for high-speed coatings; a promising model for physics of dynamic contact line on real materials with variable hydrophobicity and diverse contact angle hysteresis | [68,109,110,111,112,113,153] |
Brochard-Wyart and de Gennes | Similar to combined hydrodynamics–molecular kinetic theory; receding dynamic contact line is an irreversible process with energy dissipation caused by out-of-balance surface tension and contact line speed; the equation is obtained considering energy loss due to viscous flow near the contact line and friction force; the equation is valid for flow at low capillary numbers | [110,111] |
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Mohammad Karim, A.; Suszynski, W.J. Physics of Dynamic Contact Line: Hydrodynamics Theory versus Molecular Kinetic Theory. Fluids 2022, 7, 318. https://doi.org/10.3390/fluids7100318
Mohammad Karim A, Suszynski WJ. Physics of Dynamic Contact Line: Hydrodynamics Theory versus Molecular Kinetic Theory. Fluids. 2022; 7(10):318. https://doi.org/10.3390/fluids7100318
Chicago/Turabian StyleMohammad Karim, Alireza, and Wieslaw J. Suszynski. 2022. "Physics of Dynamic Contact Line: Hydrodynamics Theory versus Molecular Kinetic Theory" Fluids 7, no. 10: 318. https://doi.org/10.3390/fluids7100318
APA StyleMohammad Karim, A., & Suszynski, W. J. (2022). Physics of Dynamic Contact Line: Hydrodynamics Theory versus Molecular Kinetic Theory. Fluids, 7(10), 318. https://doi.org/10.3390/fluids7100318