1,973 research outputs found
Discrete solution of the electrokinetic equations
We present a robust scheme for solving the electrokinetic equations. This
goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete
solution of the convection-diffusion equation for the different charged and
neutral species that compose the fluid. The method is based on identifying the
elementary fluxes between nodes, which ensures the absence of spurious fluxes
in equilibrium. We show how the model is suitable to study electro-osmotic
flows. As an illustration, we show that, by introducing appropriate dynamic
rules in the presence of solid interfaces, we can compute the sedimentation
velocity (and hence the sedimentation potential) of a charged sphere. Our
approach does not assume linearization of the Poisson-Boltzmann equation and
allows us for a wide variation of the Peclet number.Comment: 24 pages, 7 figure
Challenges and progress on the modelling of entropy generation in porous media: a review
Depending upon the ultimate design, the use of porous media in thermal and chemical systems can provide significant operational advantages, including helping to maintain a uniform temperature distribution, increasing the heat transfer rate, controlling reaction rates, and improving heat flux absorption. For this reason, numerous experimental and numerical investigations have been performed on thermal and chemical systems that utilize various types of porous materials. Recently, previous thermal analyses of porous materials embedded in channels or cavities have been re-evaluated using a local thermal non-equilibrium (LTNE) modelling technique. Consequently, the second law analyses of these systems using the LTNE method have been a point of focus in a number of more recent investigations. This has resulted in a series of investigations in various porous systems, and comparisons of the results obtained from traditional local thermal equilibrium (LTE) and the more recent LTNE modelling approach. Moreover, the rapid development and deployment of micro-manufacturing techniques have resulted in an increase in manufacturing flexibility that has made the use of these materials much easier for many micro-thermal and chemical system applications, including emerging energy-related fields such as micro-reactors, micro-combustors, solar thermal collectors and many others. The result is a renewed interest in the thermal performance and the exergetic analysis of these porous thermochemical systems. This current investigation reviews the recent developments of the second law investigations and analyses in thermal and chemical problems in porous media. The effects of various parameters on the entropy generation in these systems are discussed, with particular attention given to the influence of local thermodynamic equilibrium and non-equilibrium upon the second law performance of these systems. This discussion is then followed by a review of the mathematical methods that have been used for simulations. Finally, conclusions and recommendations regarding the unexplored systems and the areas in the greatest need of further investigations are summarized
Phase separating binary fluids under oscillatory shear
We apply lattice Boltzmann methods to study the segregation of binary fluid
mixtures under oscillatory shear flow in two dimensions. The algorithm allows
to simulate systems whose dynamics is described by the Navier-Stokes and the
convection-diffusion equations. The interplay between several time scales
produces a rich and complex phenomenology. We investigate the effects of
different oscillation frequencies and viscosities on the morphology of the
phase separating domains. We find that at high frequencies the evolution is
almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low
viscosity) and diffusive (high viscosity) regimes, respectively. When the
period of the applied shear flow becomes of the same order of the relaxation
time of the shear velocity profile, anisotropic effects are clearly
observable. In correspondence with non-linear patterns for the velocity
profiles, we find configurations where lamellar order close to the walls
coexists with isotropic domains in the middle of the system. For particular
values of frequency and viscosity it can also happen that the convective
effects induced by the oscillations cause an interruption or a slowing of the
segregation process, as found in some experiments. Finally, at very low
frequencies, the morphology of domains is characterized by lamellar order
everywhere in the system resembling what happens in the case with steady shear.Comment: 1 table and 12 figures in .gif forma
On anisotropy function in crystal growth simulations using Lattice Boltzmann equation
In this paper, we present the ability of the Lattice Boltzmann (LB) equation,
usually applied to simulate fluid flows, to simulate various shapes of
crystals. Crystal growth is modeled with a phase-field model for a pure
substance, numerically solved with a LB method in 2D and 3D. This study focuses
on the anisotropy function that is responsible for the anisotropic surface
tension between the solid phase and the liquid phase. The anisotropy function
involves the unit normal vectors of the interface, defined by gradients of
phase-field. Those gradients have to be consistent with the underlying lattice
of the LB method in order to avoid unwanted effects of numerical anisotropy.
Isotropy of the solution is obtained when the directional derivatives method,
specific for each lattice, is applied for computing the gradient terms. With
the central finite differences method, the phase-field does not match with its
rotation and the solution is not any more isotropic. Next, the method is
applied to simulate simultaneous growth of several crystals, each of them being
defined by its own anisotropy function. Finally, various shapes of 3D crystals
are simulated with standard and non standard anisotropy functions which favor
growth in -, - and -directions
Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study
The characteristics of the hydro-thermal flow which occurs when a cold fluid
is injected into a hot fractured bedrock depend on the morphology of the
fracture. We consider a sharp triangular asperity, invariant in one direction,
perturbing an otherwise flat fracture. We investigate its influence on the
macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low
Reynolds number. In this study, numerical simulations are done with a coupled
lattice Boltzmann method that solves both the complete Navier-Stokes and
advection-diffusion equations in three dimensions. The results are compared
with those obtained under lubrication approximations which rely on many
hypotheses and neglect the three-dimensional (3D) effects. The lubrication
results are obtained by analytically solving the Stokes equation and a
two-dimensional (integrated over the thickness) advection-diffusion equation.
We use a lattice Boltzmann method with a double distribution (for mass and
energy transport) on hypercubic and cubic lattices. Beyond some critical slope
for the boundaries, the velocity profile is observed to be far from a quadratic
profile in the vicinity of the sharp asperity: the fluid within the triangular
asperity is quasi-static. We find that taking account of both the 3D effects
and the cooling of the rock, are important for the thermal exchange. Neglecting
these effects with lubrication approximations results in overestimating the
heat exchange efficiency. The evolution of the temperature over time, towards
steady state, also shows complex behavior: some sites alternately reheat and
cool down several times, making it difficult to forecast the extracted heat.Comment: In Journal of Geophysical Research B (2013) online firs
Numerical electrokinetics
A new lattice method is presented in order to efficiently solve the
electrokinetic equations, which describe the structure and dynamics of the
charge cloud and the flow field surrounding a single charged colloidal sphere,
or a fixed array of such objects. We focus on calculating the electrophoretic
mobility in the limit of small driving field, and systematically linearise the
equations with respect to the latter. This gives rise to several subproblems,
each of which is solved by a specialised numerical algorithm. For the total
problem we combine these solvers in an iterative procedure. Applying this
method, we study the effect of the screening mechanism (salt screening vs.
counterion screening) on the electrophoretic mobility, and find a weak
non-trivial dependence, as expected from scaling theory. Furthermore, we find
that the orientation of the charge cloud (i. e. its dipole moment) depends on
the value of the colloid charge, as a result of a competition between
electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter
(proceedings of the 2012 CODEF conference
Melting heat transfer analysis on magnetohydrodynamics buoyancy convection in an enclosure : a numerical study
Therollof melting heat transfer on magnetohydrodynamic natural convection in a square enclosurewithheatingof the bottom wall is examinednumericallyin this article.The dimensionlessgoverning partial differential equations are transformed into vorticity and stream functionformulationand then solved using the finite difference method(FDM). The effects of thermal Rayleigh number(Ra), melting parameter(M) and Hartmann number(Ha) are illustrated graphically.With an increasing melting parameter and Rayleigh number, the rate of fluid flow and temperature gradients are seen to increase. And in the presence of magnetic field, the temperature gradient reduces and hence the conductionmechanism dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameterin the both cases of heating of bottom wall
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