Contact angles

Merchant, G. J.; Keller, Joseph B.

doi:10.1063/1.858320

Cited by 44 publications

(73 citation statements)

References 11 publications

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“…Surprisingly, these arrived at contradicting conclusions. Merchant and Keller [5] derived a nonlocal integral equation for the interface profile that has essentially the same structure as in [8]. From asymptotic analysis they showed that the profile macroscopically approaches Young's angle, while the inner structure of the contact line displayed nontrivial oscillations.…”

Section: Introductionmentioning

confidence: 99%

“…Inspection of the integrals reveals that these are simply the potential energy per unit volume at the free surface, due to the presence of liquid and solid molecules. The equilibrium condition is thus that h(x) is an equipotential [5,30]. Mechanically, a gradient in potential energy would lead to fluid motion.…”

Section: Microscopic Free Energy and Capillary Pressurementioning

confidence: 99%

“…When approaching the contact line where the three interfaces meet, the geometry changes dramatically and the force balance can no longer be expressed in terms of surface tensions. Instead, the interface deforms at small scales to establish a nontrivial equilibrium shape [4,5]. Macrocopically, however, one recovers a wedge of angle θ Y [6].…”

Section: Introductionmentioning

confidence: 99%

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A microscopic view on contact angle selection

2008

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We discuss the equilibrium condition for a liquid that partially wets a solid on the level of intermolecular forces. Using a mean field continuum description, we generalize the capillary pressure from variation of the free energy and show at what length scale the equilibrium contact angle is selected. After recovering Young's law for homogeneous substrates, it is shown how hysteresis of the contact angle can be incorporated in a self-consistent fashion. In all cases the liquid-vapor interface takes a nontrivial shape, which is compared to models using a disjoining pressure.

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Section: Introductionmentioning

confidence: 99%

Section: Microscopic Free Energy and Capillary Pressurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A microscopic view on contact angle selection

2008

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“…Immiscible two-phase flow in the vicinity of the contact line (CL), where the fluid-fluid interface intersects the solid wall, is a classical problem that falls beyond the framework of conventional hydrodynamics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. In particular, molecular dynamics (MD) studies have shown relative slipping between the fluids and the wall, in violation of the no-slip boundary conditions [6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Generalized Navier Boundary Condition for the Moving Contact Line

Quian¹,

Sheng²,

Wang³

2003

Communications in Mathematical Sciences

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Abstract. From molecular dynamics simulations on immiscible flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the CahnHilliard interfacial free energy. Our hydrodynamic model yields near-complete slip of the contact line, with interfacial and velocity profiles matching quantitatively with those from the molecular dynamics simulations. IntroductionImmiscible two-phase flow in the vicinity of the contact line (CL), where the fluid-fluid interface intersects the solid wall, is a classical problem that falls beyond the framework of conventional hydrodynamics [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. In particular, molecular dynamics (MD) studies have shown relative slipping between the fluids and the wall, in violation of the no-slip boundary conditions [6,7,8,9]. While there have been numerous ad-hoc models [1,10,12,13,14] to address this phenomenon, none has been able to give a quantitative account of the MD slip velocity profile in the molecular-scale vicinity of the CL. This failure casts doubts on the general applicability of the continuum hydrodynamics in the CL region. In particular, a (possible) breakdown in the hydrodynamic description for the molecular-scale CL region has been suggested [8,9].Without a continuum hydrodynamic formulation, it becomes difficult or impossible to have realistic simulations of micro-or nanofluidics, or of immiscible flows in porous media where the relative wetting characteristics, the moving CL dissipation, and behavior over undulating surfaces may have macroscopic implications.From MD simulations on immiscible two-phase flows, we report the finding that the generalized Navier boundary condition (GNBC) applies for all boundary regions, whereby the relative slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluidfluid interface from its static configuration [12]. By combining GNBC with the CahnHilliard (CH) hydrodynamic formulation of two-phase flow [13,14], we obtained a consistent, continuum description of immiscible flow with predictions matching those from MD simulations. Our findings suggest the no-slip boundary condition to be an approximation to the GNBC, accurate for most macroscopic flows but failing in immiscible flows. Molecular dynamics simulationsThe MD simulations were performed for both the static and dynamic configurations in Couette and Poiseuille flows [15]. The two immiscible fluids were confined *

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“…The boundary conditions are expressed at the same time on different surfaces by dynamic Laplace formulae, but also on the contact-line by a differential equation using the new term of line viscosity. This differential equation, namely the expression of the Young-Dupré condition of the dynamic contact angle, takes into account the line viscosity but also the inhomogeneousness of all types on the solid surface [9][10][11][12]. It gives the microscopic behaviour of the Young contact angle.…”

Section: Introductionmentioning

confidence: 99%

The wetting problem of fluids on solid surfaces: Dynamics of lines and contact angle hysteresis

Gouin

2001

J. Phys. IV France

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In 1805, Young was the first who introduced an expression for contact angle in static, but today, the motion of the contact-line formed at the intersection of two immiscible fluids and a solid is still subject to dispute. By means of the new physical concept of line viscosity, the equations of motions and boundary conditions for fluids in contact on a solid surface together with interface and contact-line are revisited. A new Young-Dupré equation for the dynamic contact angle is deduced. The interfacial energies between fluids and solid take into account the chemical heterogeneities and the solid surface roughness. A scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation allows us to obtain a new macroscopic equation for the motion of the contact-line.Here we show that our theoretical predictions fit perfectly together with the contact angle hysteresis phenomenon and the experimentally well-known results expressing the dependence of the dynamic contact angle on the celerity of the contact-line. We additively get a quantitative explanation for the maximum speed of wetting (and dewetting).

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Contact angles

Cited by 44 publications

References 11 publications

A microscopic view on contact angle selection

A microscopic view on contact angle selection

Generalized Navier Boundary Condition for the Moving Contact Line

The wetting problem of fluids on solid surfaces: Dynamics of lines and contact angle hysteresis

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