Statics and dynamics of a cylindrical droplet under an external body force

Servantie, James; Müller, Marcus

doi:10.1063/1.2813415

Cited by 42 publications

(112 citation statements)

References 58 publications

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“…Firstly, it would be interesting to investigate how the two scaling regimes for contact line slip in diffuse interface models affect more complex flow problems, such as the macroscopic dynamics of a liquid droplet (Servantie & Muller 2008;Mognetti, Kusumaatmaja & Yeomans 2010;Thampi, Adhikari & Govindarajan 2013) or the criterion for the liquid entrainment (wetting failure) (Eggers 2004;Sbragaglia, Sugiyama & Biferale 2008), and whether similar renormalization of the slip length is adequate to account for their differences, as for the Poiseuille flow considered here. In these cases, we need to implement non-neutral wetting boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

Moving contact line dynamics: from diffuse to sharp interfaces

2015

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We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_D= (M\eta)^{1/2}$, where $\eta$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_D/l$ we find a diffuse interface regime in which the slip length scales as $\xi \sim(l_Dl)^{1/2}$. For larger $l_D/l>1$ we find a sharp interface regime in which the slip length depends only on the diffusive length, $\xi \sim l_D \sim (M\eta)^{1/2}$, and therefore only on the macroscopic variables $\eta$ and $M$, independent of the microscopic interfacial width $l$. We also give evidence that modifying the microscopic interfacial terms in the model's free energy functional appears to affect the value of the slip length only the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of \cite{Cox1986}, provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artifacts.Comment: 24 pages, 5 figure

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Section: Discussionmentioning

confidence: 99%

Moving contact line dynamics: from diffuse to sharp interfaces

2015

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“…This effect can be greatly reduced by considering cylindrical droplets that span the simulation box in one direction via the periodic boundary condition. In this case, the length of the three-phase contact line is twice the width of the system independent from the droplet size or contact angle [123].…”

Section: Length and Energy Scales Of Minimal Coarse-grained Models Fmentioning

confidence: 99%

Molecular Simulation of Polymer Melts and Blends: Methods, Phase Behavior, Interfaces, and Surfaces

Virnau

Binder

Heinz

et al. 2010

Encyclopedia of Polymer Blends

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Understanding thermodynamic properties, including also the phase behavior of poly mer solutions, polymer melts, and blends, has been a long-standing challenge [1][2][3][4][5][6][7]. Initially, the theoretical description was based on the lattice model introduced by Flory and Huggins [1][2][3][4][5][6][7]. In this model, a flexible macromolecule is represented by a (self-avoiding) random walk on a (typically simple cubic) lattice, such that each bead of the polymer takes one node of the lattice, and a bond between neighboring beads of the chain molecule takes a link of the lattice. For a binary polymer blend (A,B), two types of chains occur on the lattice (and possibly also free volume or vacant sites, which we denote as ). The model (normally) does not take into account any disparity in size and shape of the (effective) monomeric units of the two partners of a polymer mixture. Between (nearest neighbor) pairs AA, AB, and BB of effective monomers, pairwise interaction energies, e AA , e AB and e BB , are assumed. Thus, this model dis regards all chemical detail (as would be embodied in the atomistic modeling [8-10], where different torsional potentials and bond-angle potentials of the two constituents can describe different chain stiffness).Despite the simplicity of this lattice model, it is still a formidable problem of statistical mechanics, and its numerically exact treatment already requires largescale Monte Carlo simulations [11][12][13]. Consequently, the standard approach has been [1-7] to treat this Flory-Huggins lattice model in mean-field approximation, which leads to the following expression for the excess free energy density of mixing [4]:1:1Here w A , w B and w V 1 w B are the volume fractions of monomers of type A, B and of vacant sites, respectively. Every lattice site has to be taken by either w A Edited by Avraam I. Isayev

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“…Das & Das 2009) and molecular dynamics simulations (e.g. Servantie & Müller 2008;Hong, Ha & Balachandar 2009 for a horizontal body force, which is reminiscent of the gravitational component parallel to the inclined substrate, or equivalently for vertical substrates). Regarding the analysis of 2D droplets, we note the study of Hocking (1981), in which he considered the linearized dynamics with slip and imposed hysteresis effects, and the study by Durbin (1988), who considered a yield stress boundary condition to justify the pinning of the droplet.…”

Section: Introductionmentioning

confidence: 99%

Droplet motion on inclined heterogeneous substrates

Savva

Kalliadasis

2013

J. Fluid Mech.

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We consider the static and dynamic behaviour of two-dimensional droplets on inclined heterogeneous substrates. We utilize an evolution equation for the droplet thickness based on the long-wave approximation of the Stokes equations in the presence of slip. Through a singular perturbation procedure, evolution equations for the location of the two moving fronts are obtained under the assumption of quasistatic dynamics. The deduced equations, which are verified by direct comparisons with numerical solutions to the governing equation, are scrutinized in a variety of dynamic and equilibrium settings. For example, we demonstrate the possibility for stick-slip dynamics, substrate-induced hysteresis, the uphill motion of the droplet for sufficiently strong chemical gradients and the existence of a critical inclination angle beyond which the droplet can no longer be supported at equilibrium. Where possible, analytical expressions are obtained for various quantities of interest, which are also verified by appropriate numerical experiments.

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Statics and dynamics of a cylindrical droplet under an external body force

Cited by 42 publications

References 58 publications

Moving contact line dynamics: from diffuse to sharp interfaces

Moving contact line dynamics: from diffuse to sharp interfaces

Molecular Simulation of Polymer Melts and Blends: Methods, Phase Behavior, Interfaces, and Surfaces

Droplet motion on inclined heterogeneous substrates

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