Evaporative deposition patterns: spatial dimensions of the deposit.

By Y. Popov. Physical review. E, Statistical, nonlinear, and soft matter physics, 2004

635 citations recorded by the source corpus.

A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding evaporative deposition and may be useful for creating controlled deposition patterns.

Subfields: Biomedical Engineering, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/a2a94cefde2a05e43a82a4bf08473c37e75302ba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

A mathematical model for the evaporation of a thin sessile liquid droplet: Comparison between experiment and theory (2008, background): “Assuming that transport of vapour in the atmosphere is dominated by diffusion (see, for example, Popov [6]), the concentration of vapour in the atmosphere above the droplet and the substrate, denoted by c = c(r, z, t), satisfies Laplace’s equation, ∇c = 0.”
Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking (2017, methodology): “imental data. For comparison, also the corresponding isothermal simulation, i.e. without considering thermal eects, is indicated. This simulation, which resembles the result of the model equation by Popov (2005), predicts a noticeably faster drying than the experiment. Thus, even for pure droplets e”
Surface nanobubbles and nanodroplets (2015, background): “The same pinning assumption has also been made for evaporating (Deegan et al., 1997; Hu and Larson, 2002; Popov, 2005; Li, Butt, and Graf, 2006; Schönfeld et al., 2008; Marin et al., 2011) or dissolving (Zhang, Wang et al.”
Evaporation of water: evaporation rate and collective effects (2016, positive): “(2.5) Comparing to (2.3) with r= 0, we find a slightly simplified, yet otherwise equivalent form of (A 8) of Popov (2005), taking only evaporation into the upper half-plane into account: J = 4πDcsR ∫ ∞ 0 cosh θτ cosh πτ cosh(π− θ)τ dτ .”
Contribution of convective transport to evaporation of sessile droplets: Empirical model (2016, background): “The rate of evaporation is then expressed by the equation below [5,12]:”
Bubble puzzles: From fundamentals to applications (2018, methodology): “[135] and a critical lateral extension Lc = 4σ/P0 ≈ 2.”