19,063 research outputs found
Fluctuations of elastic interfaces in fluids: Theory and simulation
We study the dynamics of elastic interfaces-membranes-immersed in thermally
excited fluids. The work contains three components: the development of a
numerical method, a purely theoretical approach, and numerical simulation. In
developing a numerical method, we first discuss the dynamical coupling between
the interface and the surrounding fluids. An argument is then presented that
generalizes the single-relaxation time lattice-Boltzmann method for the
simulation of hydrodynamic interfaces to include the elastic properties of the
boundary. The implementation of the new method is outlined and it is tested by
simulating the static behavior of spherical bubbles and the dynamics of bending
waves. By means of the fluctuation-dissipation theorem we recover analytically
the equilibrium frequency power spectrum of thermally fluctuating membranes and
the correlation function of the excitations. Also, the non-equilibrium scaling
properties of the membrane roughening are deduced, leading us to formulate a
scaling law describing the interface growth, W^2(L,T)=L^3 g[t/L^(5/2)], where
W, L and T are the width of the interface, the linear size of the system and
the temperature respectively, and g is a scaling function. Finally, the
phenomenology of thermally fluctuating membranes is simulated and the frequency
power spectrum is recovered, confirming the decay of the correlation function
of the fluctuations. As a further numerical study of fluctuating elastic
interfaces, the non-equilibrium regime is reproduced by initializing the system
as an interface immersed in thermally pre-excited fluids.Comment: 15 pages, 11 figure
Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
We present a mesoscopic model, based on the Boltzmann Equation, for the
interaction between a solid wall and a non-ideal fluid. We present an analytic
derivation of the contact angle in terms of the surface tension between the
liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency
of the contact angle on the two free parameters of the model, which determine
the interaction between the fluid and the boundaries, i.e. the equivalent of
the wall density and of the wall-fluid potential in Molecular Dynamics studies.
We compare the analytical results obtained in the hydrodynamical limit for
the density profile and for the surface tension expression with the numerical
simulations. We compare also our two-phase approach with some exact results for
a pure hydrodynamical incompressible fluid based on Navier-Stokes equations
with boundary conditions made up of alternating slip and no-slip strips.
Finally, we show how to overcome some theoretical limitations connected with a
discretized Boltzmann scheme and we discuss the equivalence between the surface
tension defined in terms of the mechanical equilibrium and in terms of the
Maxwell construction.Comment: 29 pages, 12 figure
Lattice Boltzmann simulations of segregating binary fluid mixtures in shear flow
We apply lattice Boltzmann method to study the phase separation of a
two-dimensional binary fluid mixture in shear flow. The algorithm can simulate
systems described by the Navier-Stokes and convection-diffusion equations. We
propose a new scheme for imposing the shear flow which has the advantage of
preserving mass and momentum conservation on the boundary walls without
introducing slip velocities. Our main results concern the presence of two
typical lenght scales in the phase separation process, corresponding to domains
with two different thicknesses. Our simulations at low viscosity confirm
previous results only valid in the limit of infinite viscosity.Comment: 32 pages, 7 figure
Direct simulation of liquid-gas-solid flow with a free surface lattice Boltzmann method
Direct numerical simulation of liquid-gas-solid flows is uncommon due to the
considerable computational cost. As the grid spacing is determined by the
smallest involved length scale, large grid sizes become necessary -- in
particular if the bubble-particle aspect ratio is on the order of 10 or larger.
Hence, it arises the question of both feasibility and reasonability. In this
paper, we present a fully parallel, scalable method for direct numerical
simulation of bubble-particle interaction at a size ratio of 1-2 orders of
magnitude that makes simulations feasible on currently available
super-computing resources. With the presented approach, simulations of bubbles
in suspension columns consisting of more than fully resolved
particles become possible. Furthermore, we demonstrate the significance of
particle-resolved simulations by comparison to previous unresolved solutions.
The results indicate that fully-resolved direct numerical simulation is indeed
necessary to predict the flow structure of bubble-particle interaction problems
correctly.Comment: submitted to International Journal of Computational Fluid Dynamic
Generalized Lattice Boltzmann Method with multi-range pseudo-potential
The physical behaviour of a class of mesoscopic models for multiphase flows
is analyzed in details near interfaces. In particular, an extended
pseudo-potential method is developed, which permits to tune the equation of
state and surface tension independently of each other. The spurious velocity
contributions of this extended model are shown to vanish in the limit of high
grid refinement and/or high order isotropy. Higher order schemes to implement
self-consistent forcings are rigorously computed for 2d and 3d models. The
extended scenario developed in this work clarifies the theoretical foundations
of the Shan-Chen methodology for the lattice Boltzmann method and enhances its
applicability and flexibility to the simulation of multiphase flows to density
ratios up to O(100)
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