The nascent coffee ring: how solute diffusion counters advection

Moore, M. R.; Vella, Dominic; Oliver, James M.

doi:10.1017/jfm.2021.463

Cited by 20 publications

(96 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present work, we extend our recent analysis (Moore, Vella & Oliver 2021) to gain an understanding of the early stages of coffee-ring formation for arbitrary contact line geometries. In the model of Deegan et al.…”

Section: Introductionmentioning

confidence: 79%

“…(2000), Freed-Brown (2015) and Moore et al. (2021), since the droplet is assumed to be thin, to leading order the fluid flows within the drop according to the lubrication equations given by for , , where . Here, is the leading-order depth-averaged velocity of the droplet, the leading-order pressure is independent of , and the capillary number is Equations (2.4) are supplemented by boundary conditions that require the droplet thickness to vanish and there to be no flux of liquid through the pinned contact line, so that where is the outward pointing unit normal to , while we must prescribe the initial droplet profile, say, so that …”

Section: Formulation Of the Mathematical Modelmentioning

confidence: 99%

“…Moore et al. (2021) exploited this relative simplicity to construct consistent composite predictions for the solute mass profile. However, once axisymmetry is broken, the problem becomes much more challenging analytically and this approach is no longer feasible.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis

2022

Self Cite

View full text Add to dashboard Cite

We consider the effect of droplet geometry on the early-stages of coffee-ring formation during the evaporation of a thin droplet with an arbitrary simple, smooth, pinned contact line. We perform a systematic matched asymptotic analysis of the small capillary number, large solutal Péclet number limit for two different evaporative models: a kinetic model, in which the evaporative flux is effectively constant across the droplet, and a diffusive model, in which the flux is singular at the contact line. For both evaporative models, solute is transported to the contact line by a capillary flow in the droplet bulk, while local to the contact line, solute diffusion counters advection. The resulting interplay leads to the formation of the nascent coffee-ring profile. By exploiting a coordinate system embedded in the contact line, we solve explicitly the local leading-order problem, deriving a similarity profile (in the form of a gamma distribution) that describes the nascent coffee ring. Notably, for an arbitrary contact line geometry, the ring characteristics change due to the concomitant asymmetry in the shape of the droplet free surface, the evaporative flux (for diffusive evaporation) and the mass flux into the contact line. We utilize the asymptotic model to determine the effects of contact line geometry on the growth of the coffee ring for a droplet with an elliptical contact set. Our results offer mechanistic insight into the effect of contact line curvature on the development of the coffee ring from deposition up to jamming of the solute; moreover, our model predicts when finite concentration effects become relevant.

show abstract

Section: Introductionmentioning

confidence: 79%

Section: Formulation Of the Mathematical Modelmentioning

confidence: 99%

See 1 more Smart Citation

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…Much theoretical, numerical, and experimental research has been devoted to the effect in the last quarter century (see Ref. [ 44 ] and references therein). It is common to use equilibrium concepts like Einstein’s Fluctuation-Dissipation theorem when trying to account for the phenomenon.…”

Section: Discussionmentioning

confidence: 99%

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath

Yuvan

Bier

2022

Entropy

View full text Add to dashboard Cite

The standard textbooks contain good explanations of how and why equilibrium thermodynamics emerges in a reservoir with particles that are subjected to Gaussian noise. However, in systems that convert or transport energy, the noise is often not Gaussian. Instead, displacements exhibit an α-stable distribution. Such noise is commonly called Lévy noise. With such noise, we see a thermodynamics that deviates from what traditional equilibrium theory stipulates. In addition, with particles that can propel themselves, so-called active particles, we find that the rules of equilibrium thermodynamics no longer apply. No general nonequilibrium thermodynamic theory is available and understanding is often ad hoc. We study a system with overdamped particles that are subjected to Lévy noise. We pick a system with a geometry that leads to concise formulae to describe the accumulation of particles in a cavity. The nonhomogeneous distribution of particles can be seen as a dissipative structure, i.e., a lower-entropy steady state that allows for throughput of energy and concurrent production of entropy. After the mechanism that maintains nonequilibrium is switched off, the relaxation back to homogeneity represents an increase in entropy and a decrease of free energy. For our setup we can analytically connect the nonequilibrium noise and active particle behavior to entropy decrease and energy buildup with simple and intuitive formulae.

show abstract

“…Understanding the underpinning dynamics of coffee ring formations remain an active research topic. An example of the many excellent publications in recent years is the study by Moore et al [758] on the effects of diffusion of solute from the pinned contact line to the bulk of the drop on the pattern formation.…”

Section: E Coffee Ring Effectmentioning

confidence: 99%

Culinary fluid mechanics and other currents in food science

Mathijssen¹,

Lisicki²,

Prakash³

et al. 2022

Preprint

View full text Add to dashboard Cite

Innovations in fluid mechanics have refined food since ancient history, while creativity in cooking inspires science in return. Here, we review how recent advances in hydrodynamics are changing food science, and we highlight how the surprising phenomena that arise in the kitchen lead to discoveries and technologies across the disciplines, including rheology, soft matter, biophysics and molecular gastronomy. This review is structured like a menu, where each course highlights different aspects of culinary fluid mechanics. Our main themes include multiphase flows, complex fluids, thermal convection, hydrodynamic instabilities, viscous flows, granular matter, porous media, percolation, chaotic advection, interfacial phenomena, and turbulence. For every topic, we first provide an introduction accessible to food professionals and scientists in neighbouring fields. We then assess the state-of-the-art knowledge, the open problems, and likely directions for future research. New gastronomic ideas grow rapidly as the scientific recipes keep improving too.

show abstract

The nascent coffee ring: how solute diffusion counters advection

Abstract: Abstract

Cited by 20 publications

References 41 publications

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis

The nascent coffee ring with arbitrary droplet contact set: an asymptotic analysis

Accumulation of Particles and Formation of a Dissipative Structure in a Nonequilibrium Bath

Culinary fluid mechanics and other currents in food science

Contact Info

Product

Resources

About