3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Zhou, Chunfeng; Yue, Pengtao; Feng, James J.; Ollivier‐Gooch, Carl; Hu, Hsou Mei

doi:10.1016/j.jcp.2009.09.039

Cited by 118 publications

(75 citation statements)

References 53 publications

(89 reference statements)

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“…When CH is used to represent an interface that does not intersect a solid wall, as is the case for drop deformation, the sharp-interface limit is well established. [7][8][9] In such a limit, achieved at finite interfacial thickness ⑀, the results no longer depend on ⑀, and the diffusion across the interface becomes negligible. The results thus become comparable with sharp-interface computations and experiments, in which the interface is exceedingly thin, down to molecular scale.…”

Section: Introductionmentioning

confidence: 99%

“…To capture the interfacial profile and hence the interfacial tension accurately, the grid size needs to be at least as small as ⑀. 8,9 Thus, to simulate displacement in the 2 mm diameter capillary of Fermigier and Jenffer, 11 one must cover five or six decades of length scales, which is beyond the current computational capacity. This is analogous to the requirement in sharp-interface computations of resolving the slip length.…”

Section: Introductionmentioning

confidence: 99%

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Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

2011

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The Cahn–Hilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the near-wall layer by the relaxation of a wall energy. The first part of the paper elucidates the role of the wall relaxation in a flowing system, with two main results. First, we show that wall energy relaxation produces a dynamic contact angle that deviates from the static one, and derive an analytical formula for the deviation. Second, we demonstrate that wall relaxation competes with Cahn–Hilliard diffusion in defining the apparent contact angle, the former tending to “rotate” the interface at the contact line while the latter to “bend” it in the bulk. Thus, varying the two in coordination may compensate each other to produce the same macroscopic solution that is insensitive to the microscopic dynamics of the contact line. The second part of the paper exploits this competition to develop a computational strategy for simulating realistic flows with microscopic slip length at a reduced cost. This consists in computing a moving contact line with a diffusion length larger than the real slip length, but using the wall relaxation to correct the solution to that corresponding to the small slip length. We derive an analytical criterion for the required amount of wall relaxation, and validate it by numerical results on dynamic wetting in capillary tubes and drop spreading.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

2011

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“…With a velocity vector involved, Equation 1 can be rewritten into the complete form of the Cahn-Hilliard equation (23)(24)(25)(26)(27) as…”

Section: Coupling With Navier-stokes Equationsmentioning

confidence: 99%

Numerical Prediction of Storage Stability of Polymer-Modified Bitumen: A Coupled Model of Gravity-Driven Flow and Diffusion

Zhu

Balieu

et al. 2017

Transportation Research Record: Journal of the Transportation R

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Aiming to predict the storage stability of polymer-modified bitumen (PMB), a coupled diffusion-flow model by phase-field method is proposed in this paper. The incompressible Navier-Stokes equations are coupled with a previously developed phase-field model for PMB phase separation. The coupled model has been implemented in a finite element software package with experimentally calibrated parameters and reported data in the literature. Effects of the affecting parameters (bitumen density and dynamic viscosity) on the gravity-driven flow and phase separation in PMB are evaluated at 180 °C with the simulation results. The results indicate that the coupled diffusion-flow model is capable of predicting storage stability (and instability) of PMBs. A good correlation between the simulation results and the previously reported experimental results (storage stability tube test) has been observed. The different gravity-driven phase separation behaviours of PMBs may result from the different composition of the equilibrium phases in the PMBs as well as the different densities and dynamic viscosities of the individual components (polymer and bitumen). A bigger polymerbitumen density difference and/or a lower bitumen dynamic viscosity cause a faster flow and separation in the PMB at storage temperature. The investigated variation of bitumen dynamic viscosity has a more significant influence than the investigated variation of bitumen density in this paper, but this might depend on the specific values of the model parameters. With this study as a foundation, further experimental and numerical studies will be conducted towards storage-stable PMB binders and a more efficient test method for determining PMB storage stability. KEYWORDS:Polymer-modified bitumen; Storage stability; Phase separation; Phase-field modelling; Navier-Stokes equations Zhu, Balieu, Lu and Kringos 3 INTRODUCTION Polymer modification is an effective way to improve the properties of paving bitumen to some extent. Polymer-modified bitumen (PMB) has been widely used in road construction and maintenance in many countries. But some fundamental aspects related to the polymer modification of paving bitumen are still not fully understood today (1, 2), which may limit the sustainable application of PMB. One of the identified common issues for PMB is the potential storage instability problem (3-7). With a poor compatibility and big density difference between the polymer modifier and bitumen, the PMB may show instability during the storage and transport, i.e. the separation of the polymer-rich phase from the bitumen-rich phase.This phase separation process is controlled by many factors. Diffusion and flow may be the main mass transfer modes in this process (8). Some previous studies (9-12) have indicated that the influence of gravity due to the polymer-bitumen density difference is one of the causes for PMB phase separation in the vertical direction. However, the gravity effect might not be the direct cause for the separation but could just accelerate the possible ...

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“…With a few exceptions discussed by Zhou et al (2010), the mesh resolution necessary to mitigate the aforementioned limitations has led to the use of 2D planar or axisymmetric geometries in the majority of reported literature. Nonetheless, many engineering problems involve complex 3D geometries and multi-phase flow where 2D and 3D dynamics differ significantly (viscous encapsulation, spray formation, multi-phase micro-fluidic contactors).…”

Section: Introductionmentioning

confidence: 99%

“…Nonetheless, many engineering problems involve complex 3D geometries and multi-phase flow where 2D and 3D dynamics differ significantly (viscous encapsulation, spray formation, multi-phase micro-fluidic contactors). The inherent ability of the DI method to regularize singular events such as breakup, coalescence and moving contact lines has led to several attempts at 3D implementation within a framework that is practical both in complexity and computational cost (Badalassi et al, 2003;Jacqmin, 2004;Zhou et al, 2010). Each of these implementations has attempted to either minimize the number of cells across the interface using high-order and spectral discretization, or minimize the total mesh size through adaptive mesh refinement in the vicinity of the interface.…”

Section: Introductionmentioning

confidence: 99%

Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

Donaldson¹,

Kirpalani²,

Macchi³

2011

International Journal of Multiphase Flow

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Diffuse interface (DI) tracking methods frequently adopt the double-well energy density function to describe the free energy variation across an interface, leading to phase interpenetration and spontaneous drop shrinkage when applied to immiscible two-phase systems. While the observed continuity losses can be limited by constraints placed on the interfacial width and mobility parameter, the associated increase in computational cost and mesh requirements has limited DI methods to 2D planar and axi-symmetric flow.Using the proposed temperature-variant simplified energy density function (TVSED), the effect of the metastable thermodynamic region on phase continuity is examined using a reduced temperature parameter, T R . The solutions obtained by the proposed DI implementation and a volume-of-fluid (VOF) based solver are discussed for two common benchmark simulations (collapse of a column of water, and droplet deformation/relaxation in simple shear). While comparable solutions are obtained from the T R = 0 and VOF simulations; the large metastable region of the more commonly used double-well function (T R = 1) promoted inter-mixing in the bulk phases, diluting the inertia transferred between impacting fluids and under-predicting deformation in shear. The fundamental mechanisms responsible for spontaneous drop shrinkage are eliminated at T R = 0, allowing for constraints on the interfacial width and mobility to be relaxed. The comparable performance of T R = 0 and VOF simulations is a promising indication of the potential for application to complex 3D flows at reduced mesh resolution relative to existing DI methods.Crown

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3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

Cited by 118 publications

References 53 publications

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

Numerical Prediction of Storage Stability of Polymer-Modified Bitumen: A Coupled Model of Gravity-Driven Flow and Diffusion

Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

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