Dynamics of sessile droplet evaporation: A comparison of the spine and the elliptic mesh generation methods

Widjaja, Ervina; Liu, Nai-Chi; Li, Mingfeng; Collins, Robert T.; Basaran, Osman A.; Harris, Michael T.

doi:10.1016/j.compchemeng.2006.06.006

Cited by 15 publications

(10 citation statements)

References 18 publications

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“…Due to the complex, coupled physics involved during colloidal drop evaporation, most theoretical and numerical models reported so far are based on assumptions such as fluid flow with negligible inertia [24,30,31,41], small wetting angle [19,24], spherical cap shape of the free surface [19,24,30,31,34,38,41,42], pinned wetting line throughout the evaporation [24, 30-35, 40, 41, 43], negligible heat transfer between the drop and the substrate [19,23,24,30,40,43] and negligible Marangoni convection [36,40,44]. Also, to the best of our knowledge, no published numerical study has considered the receding of the wetting line during colloidal drop evaporation, or the interaction of the free surface and the growing peripheral deposit -which can involve depinning i.e.…”

Section: Introductionmentioning

confidence: 99%

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

2009

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An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit.In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier-Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet-air interface. Laplace stresses and thermal Marangoni stresses are accounted for. The particle concentration is tracked by solving a continuum advection-diffusion equation. Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles. Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microsphere evaporating on respectively glass and polydimethylsiloxane substrates. Measured evaporation times, deposit shape and sizes, and flow fields are in very good agreement with the numerical results. Different V dimensionless velocity vector V = (U.V) X Concentration of particles [kg of particles/kg of solution] z axial coordinate [m] Z dimensionless axial coordinate [ 0 max, / r z ]

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Section: Introductionmentioning

confidence: 99%

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

2009

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“…3b), caused by the well‐known coffee ring effect 26. Liquid evaporating at the contact line of the drop is replenished by liquid from the interior, resulting in the convective transport of solute and small particles in the drop to the contact line 26–29. Figures 3c and 3d are magnified images of 70:30 NAP–PVP on chitosan that crystallized at 25°C and 40°C.…”

Section: Resultsmentioning

confidence: 99%

“…26 Liquid evaporating at the contact line of the drop is replenished by liquid from the interior, resulting in the convective transport of solute and small particles in the drop to the contact line. [26][27][28][29] Figures 3c and 3d are magnified images of 70:30 NAP-PVP on chitosan that crystallized at 25 • C and 40 • C. In both images, the solid formed after evaporation of the solvent, ethanol. By comparing Figures 3c and 3d, it can be seen that the 25 • C sample grew in a consistent direction and with clear edges with a feather-like morphology.…”

Section: Scanning Electron Microscopymentioning

confidence: 99%

Effect of Substrates on Naproxen-Polyvinylpyrrolidone Solid Dispersions Formed via the Drop Printing Technique

Hsu

Toth

Simpson

et al. 2013

Journal of Pharmaceutical Sciences

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“…The governing equations were solved with a finite element algorithm and the elliptic mesh generation technique, as it was implemented by Christodoulou & Scriven (1992), was used. Widjaja et al (2007) compared the spine and the elliptic mesh generation techniques for studying numerically the fluid dynamics inside an evaporating liquid sessile drop. They reported that although the spine method gives acceptable results for this particular problem, it needs denser numerical grids compared to the elliptic mesh generation technique.…”

Section: Introductionmentioning

confidence: 99%

Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure

Vlachomitrou

Pelekasis

2017

J. Fluid Mech.

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A numerical method is developed to study the dynamic behaviour of an encapsulated bubble when the viscous forces of the surrounding liquid are accounted for. The continuity and Navier–Stokes equations are solved for the liquid, whereas the coating is described as a viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed for the spatial discretization of the flow domain surrounding the bubble, with the standard staggered grid arrangement that uses biquadratic and bilinear Lagrangian basis functions for the velocity and pressure in the liquid, respectively, coupled with a superparametric scheme with $B$-cubic splines as basis functions pertaining to the location of the interface. The spine method and the elliptic mesh generation technique are used for updating the mesh points in the interior of the flow domain as the shape of the interface evolves with time, with the latter being distinctly superior in capturing severely distorted shapes. The stabilizing effect of the liquid viscosity is demonstrated, as it alters the amplitude of the disturbance for which a bubble deforms and/or collapses. For a step change in the far-field pressure the dynamic evolution of the microbubble is captured until a static equilibrium is achieved. Static shapes that are significantly compressed are captured in the post-buckling regime, leading to symmetric or asymmetric shapes, depending on the relative dilatation to bending stiffness ratio. As the external overpressure increases, shapes corresponding to all the solution families that were captured evolve to exhibit contact as the two poles approach each other. Shell viscosity prevents jet formation by relaxing compressive stresses and bending moments around the indentation generated at the poles due to shell buckling. This behaviour is conjectured to be the inception process leading to static shapes with contact regions.

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Dynamics of sessile droplet evaporation: A comparison of the spine and the elliptic mesh generation methods

Cited by 15 publications

References 18 publications

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

Effect of Substrates on Naproxen-Polyvinylpyrrolidone Solid Dispersions Formed via the Drop Printing Technique

Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure

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