55,393 research outputs found
Numerical simulations of 3D flows with moving contact lines
Flows with moving contact lines are encountered in many applications involving wetting phenomena such acid gas treatment with contacting devices, film coatings, and microfluidics. Numerically simulating flows with moving contact lines under realistic conditions is a computational challenge, because a large range of length scales is involved, and the fluid/fluid interface is generally strongly curved close to the contact line. This is due to the different physical behavior in the near vicinity of a moving contact line: a conventional no-slip formulation would lead to a singularity in the wall stress at a moving contact line. Several models have been proposed to account for the physical behavior in the near vicinity of contact lines ? herein we adopt a slip formulation, which involves a slip length parameter that is typically estimated to be nanometric, which is much smaller than the dimensions of an entire flow, even for a millimetric droplet. Direct numerical simulations (DNS) of such flows wherein the entire flow is resolved not being feasible, it is proposed here to numerically resolve the large-scale flow and part of the intermediate-scale flow whilst using a subgrid-scale model, which originates from hydrodynamic theories, to represent the unresolved part of the flow. We have developed a methodology for such large-scale simulations in 3D in the context of level-set methods. Results will be presented first for axisymmetric droplet spreading (simulated in 3D) in a regime dominated by viscous and capillary effects, with a comparison against results of DNS available in the literature. This is followed by results for axisymmetric droplet spreading (simulated in 3D) for more rapid flows, wherein inertial effects enter the contact-line region, for which excellent agreement with experimental data was obtained, both qualitatively and quantitatively. A second part of the work investigates whether such a model can be used for more complex evolution of contact lines, including effects of contact-angle hysteresis in 3D, which are also represented by our computational method. For this purpose, we consider next three-dimensional drops sliding down an inclined plane; numerical results will be demonstrated to be in good agreement with experiments. The subgrid-scale model used herein is restricted to flows with moving contact lines on planar substrates with small gravity effects compared to capillary effects. Further complexities may now be considered, involving heterogeneous substrates or higher Bond numbers, which calls for further DNS and theoretical development
Transition in a numerical model of contact line dynamics and forced dewetting
We investigate the transition to a Landau-Levich-Derjaguin film in forced
dewetting using a quadtree adaptive solution to the Navier-Stokes equations
with surface tension. We use a discretization of the capillary forces near the
receding contact line that yields an equilibrium for a specified contact angle
called the numerical contact angle. Despite the well-known
contact line singularity, dynamic simulations can proceed without any explicit
additional numerical procedure. We investigate angles from to
and capillary numbers from to where the mesh size
is varied in the range of to of the capillary length
. To interpret the results, we use Cox's theory which involves a
microscopic distance and a microscopic angle . In the numerical
case, the equivalent of is the angle and we find
that Cox's theory also applies. We introduce the scaling factor or gauge
function so that and estimate this gauge function by
comparing our numerics to Cox's theory. The comparison provides a direct
assessment of the agreement of the numerics with Cox's theory and reveals a
critical feature of the numerical treatment of contact line dynamics: agreement
is poor at small angles while it is better at large angles. This scaling factor
is shown to depend only on and the viscosity ratio . In the
case of small , we use the prediction by Eggers [Phys. Rev. Lett.,
vol. 93, pp 094502, 2004] of the critical capillary number for the
Landau-Levich-Derjaguin forced dewetting transition. We generalize this
prediction to large and arbitrary and express the critical
capillary number as a function of and . An analogy can be drawn
between and the numerical slip length.Comment: This version of the paper includes the corrections indicated in Ref.
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RAM: A Relativistic Adaptive Mesh Refinement Hydrodynamics Code
We have developed a new computer code, RAM, to solve the conservative
equations of special relativistic hydrodynamics (SRHD) using adaptive mesh
refinement (AMR) on parallel computers. We have implemented a
characteristic-wise, finite difference, weighted essentially non-oscillatory
(WENO) scheme using the full characteristic decomposition of the SRHD equations
to achieve fifth-order accuracy in space. For time integration we use the
method of lines with a third-order total variation diminishing (TVD)
Runge-Kutta scheme. We have also implemented fourth and fifth order Runge-Kutta
time integration schemes for comparison. The implementation of AMR and
parallelization is based on the FLASH code. RAM is modular and includes the
capability to easily swap hydrodynamics solvers, reconstruction methods and
physics modules. In addition to WENO we have implemented a finite volume module
with the piecewise parabolic method (PPM) for reconstruction and the modified
Marquina approximate Riemann solver to work with TVD Runge-Kutta time
integration. We examine the difficulty of accurately simulating shear flows in
numerical relativistic hydrodynamics codes. We show that under-resolved
simulations of simple test problems with transverse velocity components produce
incorrect results and demonstrate the ability of RAM to correctly solve these
problems. RAM has been tested in one, two and three dimensions and in
Cartesian, cylindrical and spherical coordinates. We have demonstrated
fifth-order accuracy for WENO in one and two dimensions and performed detailed
comparison with other schemes for which we show significantly lower convergence
rates. Extensive testing is presented demonstrating the ability of RAM to
address challenging open questions in relativistic astrophysics.Comment: ApJS in press, 21 pages including 18 figures (6 color figures
Runup and rundown generated by three-dimensional sliding masses
To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented.
To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured.
Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed
A mesoscopic model for microscale hydrodynamics and interfacial phenomena: Slip, films, and contact angle hysteresis
We present a model based on the lattice Boltzmann equation that is suitable
for the simulation of dynamic wetting. The model is capable of exhibiting
fundamental interfacial phenomena such as weak adsorption of fluid on the solid
substrate and the presence of a thin surface film within which a disjoining
pressure acts. Dynamics in this surface film, tightly coupled with
hydrodynamics in the fluid bulk, determine macroscopic properties of primary
interest: the hydrodynamic slip; the equilibrium contact angle; and the static
and dynamic hysteresis of the contact angles. The pseudo- potentials employed
for fluid-solid interactions are composed of a repulsive core and an attractive
tail that can be independently adjusted. This enables effective modification of
the functional form of the disjoining pressure so that one can vary the static
and dynamic hysteresis on surfaces that exhibit the same equilibrium contact
angle. The modeled solid-fluid interface is diffuse, represented by a wall
probability function which ultimately controls the momentum exchange between
solid and fluid phases. This approach allows us to effectively vary the slip
length for a given wettability (i.e. the static contact angle) of the solid
substrate
Molecular hydrodynamics of the moving contact line in two-phase immiscible flows
The ``no-slip'' boundary condition, i.e., zero fluid velocity relative to the
solid at the fluid-solid interface, has been very successful in describing many
macroscopic flows. A problem of principle arises when the no-slip boundary
condition is used to model the hydrodynamics of immiscible-fluid displacement
in the vicinity of the moving contact line, where the interface separating two
immiscible fluids intersects the solid wall. Decades ago it was already known
that the moving contact line is incompatible with the no-slip boundary
condition, since the latter would imply infinite dissipation due to a
non-integrable singularity in the stress near the contact line. In this paper
we first present an introductory review of the problem. We then present a
detailed review of our recent results on the contact-line motion in immiscible
two-phase flow, from MD simulations to continuum hydrodynamics calculations.
Through extensive MD studies and detailed analysis, we have uncovered the slip
boundary condition governing the moving contact line, denoted the generalized
Navier boundary condition. We have used this discovery to formulate a continuum
hydrodynamic model whose predictions are in remarkable quantitative agreement
with the MD simulation results at the molecular level. These results serve to
affirm the validity of the generalized Navier boundary condition, as well as to
open up the possibility of continuum hydrodynamic calculations of immiscible
flows that are physically meaningful at the molecular level.Comment: 36 pages with 33 figure
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