Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

Chalmers, Christopher; Smith, Roger; Archer, Andrew J.

doi:10.1088/1361-648x/aa76fd

Cited by 8 publications

(41 citation statements)

References 55 publications

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“…The bulk liquid diffusion coeficient for a 3D model very similar to that considered here, with dynamics governed by the same KMC algorithm, was determined in Ref. [17]. For temperatures in a similar range to those considered here, they obtained the result that D ≈ 2.6×10 −4 σ 2 KMC steps −1 , where x KMC steps means x attempted moves per lattice site.…”

Section: Diffusion Coefficient and Time Scalesmentioning

confidence: 56%

“…Ref. [17], we can calculate the contact angle by fitting a circle to the location of the liquid-vapour interface, which is defined as the points determined by linear interpolation between pairs of neighbouring lattice sites, where the density ρ = 0.5. Results for the contact angle determined via this method are plotted in Fig.…”

Section: Contact Angle and Static Droplet Profiles From Kmcmentioning

confidence: 99%

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Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

2019

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We present a lattice-gas (generalised Ising) model for liquid droplets on solid surfaces. The time evolution in the model involves two processes: (i) Single-particle moves which are determined by a kinetic Monte Carlo algorithm. These incorporate into the model particle diffusion over the surface and within the droplets and also evaporation and condensation, i.e. the exchange of particles between droplets and the surrounding vapour. (ii) Larger-scale collective moves, modelling advective hydrodynamic fluid motion, determined by considering the dynamics predicted by a thin-film equation. The model enables us to relate how macroscopic quantities such as the contact angle and the surface tension depend on the microscopic interaction parameters between the particles and with the solid surface. We present results for droplets joining, spreading, sliding under gravity, dewetting, the effects of evaporation, the interplay of diffusive and advective dynamics, and how all this behaviour depends on the temperature and other parameters. * Electronic address: A.J. Archer@lboro.ac.uk arXiv:1906.08121v1 [cond-mat.soft] 19 Jun 2019 is to use Monte Carlo methods to simulate the dynamic properties of Hamiltonian systems [18]. However, it is not clear to us that one should enforce detailed balance when constructing coarse grained models of such non-equilibrium systems, since droplets on surfaces are highly dissipative systems, due to the evaporation, the strong coupling to the substrate, etc. Of course, at equilibrium, there should be detailed balance in the model.To model collective hydrodynamic motion in our model, we generate large-scale collective particle moves by considering the dynamics that is predicted by a thin-film equation. This is a time evolution equation for the liquid film thickness profile h, i.e. the height of the liquid-vapour interface above the surface [2,[19][20][21][22]. This equation is derived from the Navier-Stokes equations for a film of liquid on a surface by making a long-wave approximation, which greatly simplifies the analysis. When generating these 'thin-film moves', we first determine the liquid film height profile from the configuration of occupied lattice sites, we then evolve the thin-film equation for a short amount of time, and then map back to the lattice. In our model, an important quantity is the parameter λ, defined below in Eq. (13), which is proportional to the ratio of the number of KMC attempted particle moves to the number of thin-film moves. When λ = 0, our model reduces to just evolving the thin-film equation, whilst in the limit λ → ∞, our model is a pure KMC model. Therefore, this parameter λ ∝ D/η, where D is a single-particle diffusion coefficient and η is the viscosity.Key quantities that characterises how a liquid wets a surface are the spreading parameter S = γ sv − (γ sl + γ lv ), where γ sv , γ sl , and γ lv are the solid-vapour, solid-liquid and liquid-vapour interfacial tensions, respectively [2], and also the contact angle θ, which is given by Young's equation [2]:The...

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Section: Diffusion Coefficient and Time Scalesmentioning

confidence: 56%

Section: Contact Angle and Static Droplet Profiles From Kmcmentioning

confidence: 99%

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

2019

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“…[43][44][45][46][47][48] The present DDFT assumes the same Hamiltonian as the MC model in Ref. 48. Thus, the DDFT presented here is able to fully describe any vertical variations in the local densities within the droplet, such as the formation of a nanoparticle 'crust' on the drying droplet, unlike the 2D DDFT models developed previously.…”

Section: Introductionmentioning

confidence: 99%

“…However, 3dimensional (3D) MC models have subsequently also been developed. [43][44][45][46][47][48] The present DDFT assumes the same Hamiltonian as the MC model in Ref. 48.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

2017

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We develop a lattice gas model for the drying of droplets of a nanoparticle suspension on a planar surface, using dynamical density functional theory (DDFT) to describe the time evolution of the solvent and nanoparticle density profiles. The DDFT assumes a diffusive dynamics but does not include the advective hydrodynamics of the solvent, so the model is relevant to highly viscous or near to equilibrium systems. Nonetheless, we see an equivalent of the coffee-ring stain effect, but in the present model it occurs for thermodynamic rather the fluid-mechanical reasons. The model incorporates the effect of phase separation and vertical density variations within the droplet and the consequence of these on the nanoparticle deposition pattern on the surface. We show how to include the effect of slip or no-slip at the surface and how this is related to the receding contact angle. We also determine how the equilibrium contact angle depends on the microscopic interaction parameters.

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“…A common theme in the fields of soft matter and surfacecatalyzed chemical reactions is the crucial role of mesoscopic phase separation: While soft matter deals with topics such as the demixing of lipids in bilayer membranes [1] and of polymers or nanoparticles in a melt or solution [2][3][4][5][6][7], surface catalysis relies on the structure of coexisting lowand high-density fluid domains of reactants adsorbed at a metal surface [8][9][10][11][12][13][14][15]. In this Letter, we theoretically explore under what conditions phenomenological models fail to describe phase separation in the context of surface catalysis, and discuss the implications of this failure on the morphology formation in solvent-cast thin-film polymer composites [16][17][18][19][20][21].…”

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confidence: 99%

Structuring of Fluid Adlayers upon Ongoing Unimolecular Adsorption

Schaefer

2018

Phys. Rev. Lett.

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Fluids with spatial density variations of single or mixed molecules play a key role in biophysics, soft matter and materials science. The fluid structures usually form via spinodal decomposition or nucleation following an instantaneous destabilisation of the initially disordered fluid. However, in practice an instantaneous quench is often not viable, and the rate of destabilisation may be gradual rather than instantaneous. In this work we show that the commonly used phenomenological descriptions of fluid structuring are inadequate under these conditions. We come to that conclusion in the context of surface catalysis, where we employ kinetic Monte Carlo simulations to describe the unimolecular adsorption of gaseous molecules onto a metal surface. The adsorbates diffuse at the surface and, as a consequence of lateral interactions and due to an ongoing increase of the surface coverage, phase separate into coexisting low-and high-density regions. The typical size of these regions turns out to depend much more strongly on the rate of adsorption than predicted from recently reported phenomenological models. We discuss how this finding contributes to the fundamental understanding of the crossover from liquid-liquid to liquid-solid demixing of solutioncast polymer blends.

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Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces

Cited by 8 publications

References 55 publications

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

Kinetic Monte Carlo and hydrodynamic modeling of droplet dynamics on surfaces, including evaporation and condensation

Dynamical Density Functional Theory for the Evaporation of Droplets of Nanoparticle Suspension

Structuring of Fluid Adlayers upon Ongoing Unimolecular Adsorption

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