On contact-line dynamics with mass transfer

Oliver, James M.; Whiteley, Jonathan; Saxton, Matthew; Vella, Dominic; Zubkov, V. V.; King, John R.

doi:10.1017/s0956792515000364

Cited by 14 publications

(43 citation statements)

References 43 publications

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“…Equating the rate of change of the drop volume with the total mass flux out of the drop therefore gives us the d 2 -law. We note that the d 2 -law can also arise from a one-sided model with a uniform evaporation rate, independent of d (Oliver et al 2015). Near-extinction behaviour differing slightly from the d 2 -law has also been observed (see, for example, Shahidzadeh- Bonn et al 2006).…”

Section: Introductionmentioning

confidence: 55%

“…New asymptotic methods will also need to be developed to connect the nano-scale of relevance to the contact-line physics and the macro-scale of a drop'. In the absence of evaporation, asymptotic approaches have been extremely fruitful (Lacey 1982;Hocking 1983), leading in particular to a systematic derivation of Tanner's law, and some asymptotic analysis has been carried out on mass-transfer models incorporating simple physics (Savva, Rednikov & Colinet 2014;Oliver et al 2015).…”

Section: Introductionmentioning

confidence: 99%

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On thin evaporating drops: When is the -law valid?

et al. 2016

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We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip and diffusion-dominated vapour transport are taken into account. A matched asymptotic analysis in the limit of small slip is used to derive a generalization of Tanner's law that takes account of the effect of mass transfer. We find a criterion for when the contact-set radius close to extinction evolves as the square root of the time remaining until extinction -the famous d 2 -law. However, for a sufficiently large rate of evaporation, our analysis predicts that a (slightly different) 'd 13/7 -law' is more appropriate. Our asymptotic results are validated by comparison with numerical simulations.

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Section: Introductionmentioning

confidence: 55%

Section: Introductionmentioning

confidence: 99%

On thin evaporating drops: When is the -law valid?

et al. 2016

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“…We plot the finite-Pe k solution for the evaporation rate at the contact line E(1 − ), given by (33), as a function of Pe k in Fig. 3b.…”

Section: Validation Of Asymptotic Resultsmentioning

confidence: 99%

“…In calculating the typical kinetic velocity v k from (8), we assume that the evaporation coefficient σ e = 1 and that the interfacial temperature T in is constant at 25 • C. We assume that c ∞ = 0 for each of the liquids in the table. The kinetic Péclet number Pe k = Rv k /D is given for (thin) drops with contact-set radii R = 1 mm and R = 10 µm A related quantity of interest, and a useful proxy, is the evaporation rate at the contact line, E(1 − ); the liquid motion has a strong dependence upon the size of this quantity [33]. We note that with Pe k = ∞,…”

Section: Formulationmentioning

confidence: 99%

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Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

et al. 2017

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We consider the transport of vapour caused by the evaporation of a thin, axisymmetric, partially wetting drop into an inert gas. We take kinetic effects into account through a linear constitutive law that states that the mass flux through the drop surface is proportional to the difference between the vapour concentration in equilibrium and that at the interface. Provided that the vapour concentration is finite, our model leads to a finite mass flux in contrast to the contact-line singularity in the mass flux that is observed in more standard models that neglect kinetic effects. We perform a local analysis near the contact line to investigate the way in which kinetic effects regularize the mass-flux singularity at the contact line. An explicit expression is derived for the mass flux through the free surface of the drop. A matched-asymptotic analysis is used to further investigate the regularization of the mass-flux singularity in the physically relevant regime in which the kinetic timescale is much smaller than the diffusive one. We find that the effect of kinetics is limited to an inner region near the contact line, in which kinetic effects enter at leading order and regularize the mass-flux singularity. The inner problem is solved explicitly using the Wiener-Hopf method and a uniformly valid composite expansion is derived for the mass flux in this asymptotic limit.

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Evaporation effects in elastocapillary aggregation

Hadjittofis¹,

Lister

Singh³

et al. 2016

J. Fluid Mech.

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We consider the effect of evaporation on the aggregation of a number of elastic objects due to a liquid's surface tension. In particular, we consider an array of spring-block elements in which the gaps between blocks are filled by thin liquid films that evaporate during the course of an experiment. Using lubrication theory to account for the fluid flow within the gaps, we study the dynamics of aggregation. We find that a non-zero evaporation rate causes the elements to aggregate more quickly and, indeed, to contact within finite time. However, we also show that the number of elements within each cluster decreases as the evaporation rate increases. We explain these results quantitatively by comparison with the corresponding two-body problem and discuss their relevance for controlling pattern formation in elastocapillary systems.

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On contact-line dynamics with mass transfer

Cited by 14 publications

References 43 publications

On thin evaporating drops: When is the -law valid?

On thin evaporating drops: When is the -law valid?

Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

Evaporation effects in elastocapillary aggregation

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