The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow

Cox, R. G.

doi:10.1017/s0022112086000332

Cited by 1,262 publications

(1,242 citation statements)

References 23 publications

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“…(13) is valid only for finite-thickness interfaces and implies a surface-force singularity if the interface thickness tends to zero. To eliminate the singularity the dynamic and static contact angles should be equal α = α ′ , which explains the underlying reason of Cox's hypothesis [4] for a macroscopic analysis stating that wall-slip is permitted and the contact angle is independent of contact-line velocity. A result of the surface-force balance with α = α ′ from Eq.…”

Section: Discussionmentioning

confidence: 99%

Moving Contact Line with Balanced Stress Singularities

Adams

2009

IUTAM Bookseries

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A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed, finite-width interface model. The analysis in the sharp-interface limit shows that the singularity of the viscous stress can be balanced by another singularity of the unbalanced surface stress. The dynamic contact angle is determined by surface tension, viscosity, contact-line velocity and a single non-dimensional parameter reflecting the lengthscale ratio between interface width and the thickness of the first molecule layer at the wall surface. The widely used Navier boundary condition and Cox's hypothesis are also derived following the same procedure by permitting finite-wall slip.

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Section: Discussionmentioning

confidence: 99%

Moving Contact Line with Balanced Stress Singularities

Adams

2009

IUTAM Bookseries

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“…[1][2][3] The theories of spreading can be divided into two groups in which the main difference is the identification of the primary source of energy dissipation that controls the movement of the liquid front. [3][4][5][6][7] Continuous hydrodynamic theories focus on spreading controlled by the bulk liquid's viscous impedance 5,[8][9][10] while molecularkinetic analyses describe a situation in which local dissipation at the triple line is the dominant contribution. 4,6,11,12 The relative importance of each dissipation mechanism depends on a balance between the viscosity, the activation energy for viscous flow, and the strength of the solid/liquid interactions.…”

Section: Introductionmentioning

confidence: 99%

“…Hydrodynamic theories search for a universal relationship between the dynamic contact angle and the capillary number, Ca = vη/γ lv (v is the velocity of the triple junction and η the liquid viscosity), that is typically written in the form [8][9][10] :…”

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Spreading of Viscous Liquids at High Temperature: Silicate Glasses on Molybdenum

et al. 2005

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The spreading of Si-Ca-Al-Ti-O glasses on molybdenum has been investigated. By controlling the oxygen activity in the furnace, spreading can take place under reactive or non-reactive conditions. As the nucleation of the reaction product under reactive conditions is slow in comparison to the spreading kinetics, in both cases the glass front moves on the metal surface with similar spreading velocities. Spreading can be described using a molecular dynamics model where the main contribution to the wetting activation energy comes from the viscous interactions in the liquid. Enhanced interfacial diffusions in low-oxygen activities (reactive cases) form triple-line ridges that can pin the wetting front and cause a stick-slip motion.

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“…In the first group, the bouncing process and the number of bouncing adopted; the hydrodynamic model (Cox, 1986), and the molecular kinetic does not increase strongly leading the author to suggest that the bouncing 100 process is not entirely controlled by flow properties in the liquid film. Most…”

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confidence: 99%

On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface

Albadawi

Donoghue

Robinson

et al. 2014

International Journal of Multiphase Flow

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On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface, International Journal of Multiphase Flow (2014), doi: http://dx.doi.org/10. 1016/ j.ijmultiphaseflow.2014.05.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface AbstractThe process of free rise, collision on and bounce from a solid horizontal surface for a single isolated bubble is investigated by numerical simulations based on the Volume of Fluid method (VOF). The volume fraction advection equation is solved algebraically using the compressive scheme implemented in the CFD open source library (OpenFOAM R ) using both axi-symmetrical and three dimensional domains. The solution sensitivity to the mesh refinement towards the solid boundary and the contact angle formulation (static and dynamic) are assessed with two different fluid mixtures for a range of Bond numbers [0.298 − 1.48] and two different surface hydrophilicities. Numerical results are assessed against published as well as new experiments to include both axi-symmetrical and three dimensional rise trajectories. The investigation addresses the liquid microfilm formation and drainage considering both flow and pressure fields and bubble dynamic characteristics over successive rebounds. Results highlight the importance of resolving the liquid micro layer at the interface between the gas and solid surface in particular in the case of superhydrophobic surfaces. A coarse mesh is shown to precipitate the liquid film drainage. This results in early formation of a triple phase contact line (TPCL) which can occur as soon as the first rebound whereas physical observations indicate that this typically happens much later at a stage when * Corresponding authors a significant part of the bubble kinetic energy has been dissipated following several rebounds. As a result numerical predictions are shown to be much more sensitive to the contact angle formulation than when a refined mesh allows a more accurate representation of the film drainage. In this case, static and dynamic contact angle models give broadly similar rebound characteristics. Following validation, the numerical simulations are used to provide some useful insight in the mechanisms driving the film drainage and the gas liquid interface as it interacts with the solid surface.

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The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow

Cited by 1,262 publications

References 23 publications

Moving Contact Line with Balanced Stress Singularities

Moving Contact Line with Balanced Stress Singularities

Spreading of Viscous Liquids at High Temperature: Silicate Glasses on Molybdenum

On the assessment of a VOF based compressive interface capturing scheme for the analysis of bubble impact on and bounce from a flat horizontal surface

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