6,242 research outputs found
Contact angle determination in multicomponent lattice Boltzmann simulations
Droplets on hydrophobic surfaces are ubiquitous in microfluidic applications
and there exists a number of commonly used multicomponent and multiphase
lattice Boltzmann schemes to study such systems. In this paper we focus on a
popular implementation of a multicomponent model as introduced by Shan and
Chen. Here, interactions between different components are implemented as
repulsive forces whose strength is determined by model parameters. In this
paper we present simulations of a droplet on a hydrophobic surface. We
investigate the dependence of the contact angle on the simulation parameters
and quantitatively compare different approaches to determine it. Results show
that the method is capable of modelling the whole range of contact angles. We
find that the a priori determination of the contact angle is depending on the
simulation parameters with an uncertainty of 10 to 20%.Comment: 14 pages, 7 figure
Atwood ratio dependence of Richtmyer-Meshkov flows under reshock conditions using large-eddy simulations
We study the shock-driven turbulent mixing that occurs when a perturbed planar density interface is impacted by a planar shock wave of moderate strength and subsequently reshocked. The present work is a systematic study of the influence of the relative molecular weights of the gases in the form of the initial Atwood ratio A. We investigate the cases A = ± 0.21, ±0.67 and ±0.87 that correspond to the realistic gas combinations air–CO_2, air–SF_6 and H_2–air. A canonical, three-dimensional numerical experiment, using the large-eddy simulation technique with an explicit subgrid model, reproduces the interaction within a shock tube with an endwall where the incident shock Mach number is ~1.5 and the initial interface perturbation has a fixed dominant wavelength and a fixed amplitude-to-wavelength ratio ~0.1. For positive Atwood configurations, the reshock is followed by secondary waves in the form of alternate expansion and compression waves travelling between the endwall and the mixing zone. These reverberations are shown to intensify turbulent kinetic energy and dissipation across the mixing zone. In contrast, negative Atwood number configurations produce multiple secondary reshocks following the primary reshock, and their effect on the mixing region is less pronounced. As the magnitude of A is increased, the mixing zone tends to evolve less symmetrically. The mixing zone growth rate following the primary reshock approaches a linear evolution prior to the secondary wave interactions. When considering the full range of examined Atwood numbers, measurements of this growth rate do not agree well with predictions of existing analytic reshock models such as the model by Mikaelian (Physica D, vol. 36, 1989, p. 343). Accordingly, we propose an empirical formula and also a semi-analytical, impulsive model based on a diffuse-interface approach to describe the A-dependence of the post-reshock growth rate
Lattice-Boltzmann Modelling of Immiscible Fluid Displacement in Geologic Porous Media
Over the past two decades, multicomponent lattice-Boltzmann (LB) modelling has become a popular numerical technique to study the porous medium systems. For this technique to become a mature platform at a production level and to solve realistic problem that can be readily incorporated in the digital core analysis services for the oil and gas industries, there are still some challenges to resolve. This thesis intends to resolve some of issues confronted by the LB community. The first part of the thesis investigates the impact of the fundamental trade-off between image resolution and field of view on LB modelling. This is of practical value since 3D images of geological samples rarely have both sufficient resolution to capture fine structure and sufficient field of view to capture a full representative elementary volume of the medium. To optimise the simulations, it is important to know the minimum number of grid points that LB methods require to deliver physically meaningful results, and allow for the sources of measurement uncertainty to be appropriately balanced. We choose two commonly used multicomponent LB models, Shan-Chen and Rothman-Keller models, and study the behaviour of these two models when the phase interfacial radius of curvature and the feature size of the medium approach the discrete unit size of the computational grid. Both simple, small-scale test geometries and real porous media are considered. Models' behaviour in the extreme discrete limit is classified ranging from gradual loss of accuracy to catastrophic numerical breakdown. Based on this study, we provide guidance for experimental data collection and how to apply the LB methods to accurately resolve physics of interest for two-fluid flow in porous media. Resolution effects are particularly relevant to the study of low-porosity systems, including fractured materials, when the typical pore width may only be a few voxels across. The second part of the thesis explores the two-fluid displacement mechanism, especially the Haines jump dynamics and associated snap-off during drainage, by using a novel flux boundary condition, which is numerically more stable, and can more realistically replicate experiments given a prescribed capillary number. Irreversible events such as Haines jump in multiphase flow is what ultimately determines the hysteric behaviour of the porous medium systems. The high temporal resolution of LB methods makes it a suitable candidate to capture the dynamics of fast events (e.g. Haines jump in millisecond). We study the impacts of both the geometries of porous medium using persistent homology and the dynamic factors of fluids (i.e. viscosity ratio and capillary number) on the occurrence and frequency of snap-off events during drainage
The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics
We consider the impact of surface hydrodynamics on the interplay between
curvature and composition in coarsening processes on model systems for
biomembranes. This includes scaling laws and equilibrium configurations, which
are investigated by computational studies of a surface two-phase flow problem
with additional phase-depending bending terms. These additional terms
geometrically favor specific configurations. We find that as in 2D the effect
of hydrodynamics strongly depends on the composition. In situations where the
composition allows a realization of a geometrically favored configuration, the
hydrodynamics enhances the evolution into this configuration. We restrict our
model and numerics to stationary surfaces and validate the numerical approach
with various benchmark problems and convergence studies
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
Analytical modeling of micelle growth. 2. Molecular thermodynamics of mixed aggregates and scission energy in wormlike micelles
Hypotheses: Quantitative molecular-thermodynamic theory of the growth of
giant wormlike micelles in mixed nonionic surfactant solutions can be developed
on the basis of a generalized model, which includes the classical phase
separation and mass action models as special cases. The generalized model
describes spherocylindrical micelles, which are simultaneously multicomponent
and polydisperse in size. Theory: The model is based on explicit analytical
expressions for the four components of the free energy of mixed nonionic
micelles: interfacial-tension, headgroup-steric, chain-conformation components
and free energy of mixing. The radii of the cylindrical part and the spherical
endcaps, as well as the chemical composition of the endcaps, are determined by
minimization of the free energy. Findings: In the case of multicomponent
micelles, an additional term appears in the expression for the micelle growth
parameter (scission free energy), which takes into account the fact that the
micelle endcaps and cylindrical part have different compositions. The model
accurately predicts the mean mass aggregation number of wormlike micelles in
mixed nonionic surfactant solutions without using any adjustable parameters.
The endcaps are enriched in the surfactant with smaller packing parameter that
is better accommodated in regions of higher mean surface curvature. The model
can be further extended to mixed solutions of nonionic, ionic and zwitterionic
surfactants used in personal-care and house-hold detergency
An isogeometric finite element formulation for phase transitions on deforming surfaces
This paper presents a general theory and isogeometric finite element
implementation for studying mass conserving phase transitions on deforming
surfaces. The mathematical problem is governed by two coupled fourth-order
nonlinear partial differential equations (PDEs) that live on an evolving
two-dimensional manifold. For the phase transitions, the PDE is the
Cahn-Hilliard equation for curved surfaces, which can be derived from surface
mass balance in the framework of irreversible thermodynamics. For the surface
deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation.
Both PDEs can be efficiently discretized using -continuous interpolations
without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured
spline spaces with pointwise -continuity are utilized for these
interpolations. The resulting finite element formulation is discretized in time
by the generalized- scheme with adaptive time-stepping, and it is fully
linearized within a monolithic Newton-Raphson approach. A curvilinear surface
parameterization is used throughout the formulation to admit general surface
shapes and deformations. The behavior of the coupled system is illustrated by
several numerical examples exhibiting phase transitions on deforming spheres,
tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to
the text, added supplementary movie file
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