1,411 research outputs found
Numerical approximation of a phase-field surfactant model with fluid flow
Modelling interfacial dynamics with soluble surfactants in a multiphase
system is a challenging task. Here, we consider the numerical approximation of
a phase-field surfactant model with fluid flow. The nonlinearly coupled model
consists of two Cahn-Hilliard-type equations and incompressible Navier-Stokes
equation. With the introduction of two auxiliary variables, the governing
system is transformed into an equivalent form, which allows the nonlinear
potentials to be treated efficiently and semi-explicitly. By certain subtle
explicit-implicit treatments to stress and convective terms, we construct first
and second-order time marching schemes, which are extremely efficient and
easy-to-implement, for the transformed governing system. At each time step, the
schemes involve solving only a sequence of linear elliptic equations, and
computations of phase-field variables, velocity and pressure are fully
decoupled. We further establish a rigorous proof of unconditional energy
stability for the first-order scheme. Numerical results in both two and three
dimensions are obtained, which demonstrate that the proposed schemes are
accurate, efficient and unconditionally energy stable. Using our schemes, we
investigate the effect of surfactants on droplet deformation and collision
under a shear flow, where the increase of surfactant concentration can enhance
droplet deformation and inhibit droplet coalescence
A cut finite element method for coupled bulk-surface problems on time-dependent domains
In this contribution we present a new computational method for coupled
bulk-surface problems on time-dependent domains. The method is based on a
space-time formulation using discontinuous piecewise linear elements in time
and continuous piecewise linear elements in space on a fixed background mesh.
The domain is represented using a piecewise linear level set function on the
background mesh and a cut finite element method is used to discretize the bulk
and surface problems. In the cut finite element method the bilinear forms
associated with the weak formulation of the problem are directly evaluated on
the bulk domain and the surface defined by the level set, essentially using the
restrictions of the piecewise linear functions to the computational domain. In
addition a stabilization term is added to stabilize convection as well as the
resulting algebraic system that is solved in each time step. We show in
numerical examples that the resulting method is accurate and stable and results
in well conditioned algebraic systems independent of the position of the
interface relative to the background mesh
A level-set model for two-phase flow with variable surface tension: thermocapillary and surfactants
An unstructured conservative level-set method for two-phase flow with variable surface tension is introduced. Surface tension is a function of temperature or surfactant concentration on the interface. Consequently, the called Marangoni stresses induced by temperature gradients or surfactant concentration gradients on the interface lead to a coupling of momentum transport equation with thermal energy transport equation or interface surfactant transport equation. The finite-volume method discretizes transport equations on 3D collocated unstructured meshes. The unstructured conservative level-set method is employed for interface capturing, whereas the multiple marker approach avoids the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters are proposed to discretize the convective term of transport equations. A central difference scheme discretizes diffusive terms. Gradients are evaluated by the weighted least-squares method. Verifications and validations are reportedThe main author, N. Balcazar-Arciniega, as a Serra-Húnter Fellow (UPC-LE8027), acknowledges the Catalan Government for the financial support through this programme. Simulations were executed using computing time granted by the RES (IM-2021-1-0013, IM-2020-2-0002) and PRACE 14th Call (2016153612) on the supercomputer MareNostrum IV based in Barcelona, Spain. The authors acknowledge the financial support of the MINECO, Spain (PID2020-115837RB-100).Peer ReviewedPostprint (published version
Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities
 In this work, we present a hydrodynamics coupled phase-field surfactant model with variable densities. Two scalar auxiliary variables are introduced to transform the original free energy functional into an equivalent form, and then a new thermodynamically consistent model can be obtained. In this model, evolutions of two phase-field variables are described by two Cahn-Hilliard-type equations, and the fluid flow is dominated by incompressible Navier-Stokes equation. The finite difference method on staggered grid is used to solve the above model. Then a classical droplet rising case and a droplet merging case are used to validate our model. Finally, we study the effect of surfactants on droplet deformation and merging. A more prolate profile of droplet is observed under a higher surfactant bulk concentration, which verifies the effect of surfactant in reducing the interfacial tension. Increases in surface Peclet number and initial surfactant bulk concentration can enhance the non-uniformity of surfactant distribution around the interface, which will arise the Marangoni force. The Marangoni force acts as an additional repulsive force to delay the droplet merging.Cited as: Zhu, G., Li, A. Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities. Advances in Geo-Energy Research, 2020, 4(1): 86-98, doi: 10.26804/ager.2020.01.0
Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence
We perform direct numerical simulations of surfactant-laden droplets in
homogeneous-isotropic turbulence with Taylor Reynolds number
. Effects of surfactant on the droplet and local flow
statistics are well approximated using a lower, averaged value of surface
tension, allowing us to extend the framework developed by Kolmogorov (1949) and
Hinze (1955) for surfactant-free bubbles to surfactant-laden droplets. We find
the Kolmogorov-Hinze scale () is indeed a pivotal length scale in the
droplets' dynamics, separating the coalescence-dominated and the
breakage-dominated regimes in the droplet size distribution. We see that
droplets smaller than have spheroid-like shapes, whereas larger droplets
have long convoluted filamentous shapes with diameters equal to . As a
result, droplets smaller than have areas that scale as , while
larger droplets have areas that scale as , where is the droplet
equivalent diameter. We further characterise the filamentous droplets by
computing the number of handles (loops of the dispersed phase extending into
the carrier phase) and voids (regions of the carrier phase enclosed by the
dispersed phase) on each droplet. The number of handles per unit length of
filament () scales inversely with surface tension, while the
number of voids is independent of surface tension. Handles are indeed an
unstable feature of the interface and are destroyed by the restoring effect of
surface tension, whereas voids can move freely inside the droplets.Comment: 31 pages, 13 figure
Computational analysis of single rising bubbles influenced by soluble surfactant
This paper presents novel insights about the influence of soluble surfactants
on bubble flows obtained by Direct Numerical Simulation (DNS). Surfactants are
amphiphilic compounds which accumulate at fluid interfaces and significantly
modify the respective interfacial properties, influencing also the overall
dynamics of the flow. With the aid of DNS local quantities like the surfactant
distribution on the bubble surface can be accessed for a better understanding
of the physical phenomena occurring close to the interface. The core part of
the physical model consists in the description of the surfactant transport in
the bulk and on the deformable interface. The solution procedure is based on an
Arbitrary Lagrangian-Eulerian (ALE) Interface-Tracking method. The existing
methodology was enhanced to describe a wider range of physical phenomena. A
subgrid-scale (SGS) model is employed in the cases where a fully resolved DNS
for the species transport is not feasible due to high mesh resolution
requirements and, therefore, high computational costs. After an exhaustive
validation of the latest numerical developments, the DNS of single rising
bubbles in contaminated solutions is compared to experimental results. The full
velocity transients of the rising bubbles, especially the contaminated ones,
are correctly reproduced by the DNS. The simulation results are then studied to
gain a better understanding of the local bubble dynamics under the effect of
soluble surfactant. One of the main insights is that the quasi-steady state of
the rise velocity is reached without ad- and desorption being necessarily in
local equilibrium
Effect of surfactants during drop formation in a microfluidic channel: a combined experimental and computational fluid dynamics approach
The effect of surfactants on the flow characteristics during rapid drop formation in a microchannel is investigated using high-speed imaging, micro-particle image velocimetry and numerical simulations; the latter are performed using a three- dimensional multiphase solver that accounts for the transport of soluble surfactants in the bulk and at the interface. Drops are generated in a flow-focusing microchannel, using silicone oil ( 4.6
mPa s) as the continuous phase and a 52 % w/w glycerol solution as the dispersed phase. A non-ionic surfactant (Triton X-100) is dissolved in the dispersed phase at concentrations below and above the critical micelle concentration. Good agreement is found between experimental and numerical data for the drop size, drop formation time and circulation patterns. The results reveal strong circulation patterns in the forming drop in the absence of surfactants, whose intensity decreases with increasing surfactant concentration. The surfactant concentration profiles in the bulk and at the interface are shown for all stages of drop formation. The surfactant interfacial concentration is large at the front and the back of the forming drop, while the neck region is almost surfactant free. Marangoni stresses develop away from the neck, contributing to changes in the velocity profile inside the drop
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