96 research outputs found
Universality for 2D Wedge Wetting
We study 2D wedge wetting using a continuum interfacial Hamiltonian model
which is solved by transfer-matrix methods. For arbitrary binding potentials,
we are able to exactly calculate the wedge free-energy and interface height
distribution function and, thus, can completely classify all types of critical
behaviour. We show that critical filling is characterized by strongly universal
fluctuation dominated critical exponents, whilst complete filling is determined
by the geometry rather than fluctuation effects. Related phenomena for
interface depinning from defect lines in the bulk are also considered.Comment: 4 pages, 1 figur
The prescribed mean curvature equation in weakly regular domains
We show that the characterization of existence and uniqueness up to vertical
translations of solutions to the prescribed mean curvature equation, originally
proved by Giusti in the smooth case, holds true for domains satisfying very
mild regularity assumptions. Our results apply in particular to the
non-parametric solutions of the capillary problem for perfectly wetting fluids
in zero gravity. Among the essential tools used in the proofs, we mention a
\textit{generalized Gauss-Green theorem} based on the construction of the weak
normal trace of a vector field with bounded divergence, in the spirit of
classical results due to Anzellotti, and a \textit{weak Young's law} for
-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector
fields have been now extended and moved in a self-contained paper available
at: arXiv:1708.0139
Ultrasonic measurement of the geometric parameters of gaseous voids in low gravity fluid containers
Droplet shapes on structured substrates and conformal invariance
We consider the finite-size scaling of equilibrium droplet shapes for fluid
adsorption (at bulk two-phase co-existence) on heterogeneous substrates and
also in wedge geometries in which only a finite domain of the
substrate is completely wet. For three-dimensional systems with short-ranged
forces we use renormalization group ideas to establish that both the shape of
the droplet height and the height-height correlations can be understood from
the conformal invariance of an appropriate operator. This allows us to predict
the explicit scaling form of the droplet height for a number of different
domain shapes. For systems with long-ranged forces, conformal invariance is not
obeyed but the droplet shape is still shown to exhibit strong scaling
behaviour. We argue that droplet formation in heterogeneous wedge geometries
also shows a number of different scaling regimes depending on the range of the
forces. The conformal invariance of the wedge droplet shape for short-ranged
forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.
Capillary filling with wall corrugations] Capillary filling in microchannels with wall corrugations: A comparative study of the Concus-Finn criterion by continuum, kinetic and atomistic approaches
We study the impact of wall corrugations in microchannels on the process of
capillary filling by means of three broadly used methods - Computational Fluid
Dynamics (CFD), Lattice-Boltzmann Equations (LBE) and Molecular Dynamics (MD).
The numerical results of these approaches are compared and tested against the
Concus-Finn (CF) criterion, which predicts pinning of the contact line at
rectangular ridges perpendicular to flow for contact angles theta > 45. While
for theta = 30, theta = 40 (no flow) and theta = 60 (flow) all methods are
found to produce data consistent with the CF criterion, at theta = 50 the
numerical experiments provide different results. Whilst pinning of the liquid
front is observed both in the LB and CFD simulations, MD simulations show that
molecular fluctuations allow front propagation even above the critical value
predicted by the deterministic CF criterion, thereby introducing a sensitivity
to the obstacle heigth.Comment: 25 pages, 8 figures, Langmuir in pres
Geometry dominated fluid adsorption on sculptured substrates
Experimental methods allow the shape and chemical composition of solid
surfaces to be controlled at a mesoscopic level. Exposing such structured
substrates to a gas close to coexistence with its liquid can produce quite
distinct adsorption characteristics compared to that occuring for planar
systems, which may well play an important role in developing technologies such
as super-repellent surfaces or micro-fluidics. Recent studies have concentrated
on adsorption of liquids at rough and heterogeneous substrates and the
characterisation of nanoscopic liquid films. However, the fundamental effect of
geometry has hardly been addressed. Here we show that varying the shape of the
substrate can exert a profound influence on the adsorption isotherms allowing
us to smoothly connect wetting and capillary condensation through a number of
novel and distinct examples of fluid interfacial phenomena. This opens the
possibility of tailoring the adsorption properties of solid substrates by
sculpturing their surface shape.Comment: 6 pages, 4 figure
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Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions
New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces
Hydrokinetic simulations of nanoscopic precursor films in rough channels
We report on simulations of capillary filling of high-wetting fluids in
nano-channels with and without obstacles. We use atomistic (molecular dynamics)
and hydrokinetic (lattice-Boltzmann) approaches which point out clear evidence
of the formation of thin precursor films, moving ahead of the main capillary
front. The dynamics of the precursor films is found to obey a square-root law
as the main capillary front, z^2(t) ~ t, although with a larger prefactor,
which we find to take the same value for the different geometries (2D-3D) under
inspection. The two methods show a quantitative agreement which indicates that
the formation and propagation of thin precursors can be handled at a
mesoscopic/hydrokinetic level. This can be considered as a validation of the
Lattice-Boltzmann (LB) method and opens the possibility of using hydrokinetic
methods to explore space-time scales and complex geometries of direct
experimental relevance. Then, LB approach is used to study the fluid behaviour
in a nano-channel when the precursor film encounters a square obstacle. A
complete parametric analysis is performed which suggests that thin-film
precursors may have an important influence on the efficiency of
nanochannel-coating strategies.Comment: 16 pages, 8 figures; To be published on JSTAT: Journal of statistical
mechanics: Theory and experiment
Variational Methods for Biomolecular Modeling
Structure, function and dynamics of many biomolecular systems can be
characterized by the energetic variational principle and the corresponding
systems of partial differential equations (PDEs). This principle allows us to
focus on the identification of essential energetic components, the optimal
parametrization of energies, and the efficient computational implementation of
energy variation or minimization. Given the fact that complex biomolecular
systems are structurally non-uniform and their interactions occur through
contact interfaces, their free energies are associated with various interfaces
as well, such as solute-solvent interface, molecular binding interface, lipid
domain interface, and membrane surfaces. This fact motivates the inclusion of
interface geometry, particular its curvatures, to the parametrization of free
energies. Applications of such interface geometry based energetic variational
principles are illustrated through three concrete topics: the multiscale
modeling of biomolecular electrostatics and solvation that includes the
curvature energy of the molecular surface, the formation of microdomains on
lipid membrane due to the geometric and molecular mechanics at the lipid
interface, and the mean curvature driven protein localization on membrane
surfaces. By further implicitly representing the interface using a phase field
function over the entire domain, one can simulate the dynamics of the interface
and the corresponding energy variation by evolving the phase field function,
achieving significant reduction of the number of degrees of freedom and
computational complexity. Strategies for improving the efficiency of
computational implementations and for extending applications to coarse-graining
or multiscale molecular simulations are outlined.Comment: 36 page
A Comparison of Splittings and Integral Equation Solvers for a Nonseparable Elliptic Equation
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