Three-dimensional wedge filling in ordered and disordered systems

Greenall, M. J.; Parry, A. O.; Romero-Enrique, J. M.

doi:10.1088/0953-8984/16/15/005

Cited by 22 publications

(39 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another geometry in which non-locality manifests itself directly is the linear wedge, where numerical studies based on the LGW model reveal hidden relations (wedge covariance) between wetting and filling which are naturally explained by the non-local theory [9].…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

Parry

Rascón

Bernardino

et al. 2006

J. Phys.: Condens. Matter

Self Cite

124

View full text Add to dashboard Cite

We derive a non-local effective interfacial Hamiltonian model for short-ranged wetting phenomena using a Green's function method. The Hamiltonian is characterized by a binding potential functional and is accurate to exponentially small order in the radii of curvature of the interface and the bounding wall. The functional has an elegant diagrammatic representation in terms of planar graphs which represent different classes of tube-like fluctuations connecting the interface and wall. For the particular cases of planar, spherical and cylindrical interfacial (and wall) configurations, the binding potential functional can be evaluated exactly. More generally, the non-local functional naturally explains the origin of the effective position-dependent stiffness coefficient in the smallgradient limit.

show abstract

Section: Discussionmentioning

confidence: 99%

“…This model may also be used to study adsorption at non-planar walls, and similarly resolves known difficulties associated with local effective Hamiltonian treatments [9,10].…”

Section: Introductionmentioning

confidence: 94%

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

Parry

Rascón

Bernardino

et al. 2006

J. Phys.: Condens. Matter

Self Cite

124

View full text Add to dashboard Cite

show abstract

“…Now consider fluid adsorption in a wedge geometry (ψ = tan α|x|). The NL model satisfies the necessary requirement of classical wedge covariance known from numerical studies of the microscopic model (1) [6]. Classical wedge covariance refers to the relationship between observables at MF critical wetting and MF wedge filling transitions.…”

mentioning

confidence: 99%

Nonlocality and Short-Range Wetting Phenomena

2004

View full text Add to dashboard Cite

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition. [2] are complementary approaches to the theory of confined fluids. Mean-field, non-local density functionals give an accurate description of structural properties but are unable to account correctly for long-wavelength interfacial fluctuations. To understand these it is usually necessary to employ mesoscopic interfacial Hamiltonians based on a collective coordinate l(x), measuring the local interfacial thickness. These models are essentially local in character containing a surface energy term proportional to the stiffness Σ of the unbinding interface and a binding potential function W (l). In more refined theories the stiffness also contains a position dependent term [3], Σ(l), which, it is has been argued, may drive the wetting transition first-order [4]. Despite progress over the last few years there are a number of outstanding problems particularly for wetting with short-ranged forces. In addition, recent studies of fluids in wedge-like geometries have uncovered hidden connections or wedge covariance relations between observables at planar wetting and wedge filling transitions [5], which have yet to understood at a deeper level. In this paper we argue that analogous to developments in density functional methods the general theory of short-ranged three-dimensional wetting should be formulated in terms of a non-local (NL) interfacial Hamiltonian. The model we propose directly allows for bulk-like correlations arising from tube-like fluctuations Consider a Landau-Ginzburg-Wilson Hamiltonian based on a continuum order-parameter (magnetization) m(r) in a semi-infinite geometry with bounding surface described by a single-valued height function ψ(x) where x = (x, y) is the parallel displacement vector. Denoting the surface magnetization by m 1 (x) we write (1) where ds ψ = 1 + (∇ψ) 2 dx is the wall area element whilst φ(m) and φ 1 (m 1 ) are suitable bulk and surface potentials [9]. The bulk Hamiltonian is isotropic so the interfacial tension and stiffness are the same. Following FJ we identify the interfacial modelwhere m Ξ (r) is the profile which minimises Eq. (1) subject to a given interfacial configuration. FJ determined m Ξ (r) perturbatively in terms of local planar constrained profiles [3]. He...

show abstract

“…In the mean-field approximation, the average interfacial position profile for binding potentials characterized by a critical exponent ␣ s = 0 fulfills the following generalized covariance relationship [15]:…”

Section: ͑22͒mentioning

confidence: 99%

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study

2004

View full text Add to dashboard Cite

Interfacial structure and correlation functions near a two-dimensional wedge filling transition are studied using effective interfacial Hamiltonian models. An exact solution for short range binding potentials and results for Kratzer binding potentials show that sufficiently close to the filling transition a new length scale emerges and controls the decay of the interfacial profile relative to the substrate and the correlations between interfacial positions above different positions. This new length scale is much larger than the intrinsic interfacial correlation length, and it is related geometrically to the average value of the interfacial position above the wedge midpoint. The interfacial behavior is consistent with a breather mode fluctuation picture, which is shown to emerge from an exact decimation functional renormalization group scheme that keeps the geometry invariant.

show abstract

Three-dimensional wedge filling in ordered and disordered systems

Cited by 22 publications

References 38 publications

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

Derivation of a non-local interfacial Hamiltonian for short-ranged wetting: I. Double-parabola approximation

Nonlocality and Short-Range Wetting Phenomena

Interfacial structure at a two-dimensional wedge filling transition: Exact results and a renormalization group study

Contact Info

Product

Resources

About