Abstract:When a drop is placed on a flat substrate tilted at an inclined angle, it can be deformed by gravity and its initial contact angle divides into front and rear contact angles by inclination. Here we study on evaporation dynamics of a pure water droplet on a flat solid substrate by controlling substrate inclination and measuring mass and volume changes of an evaporating droplet with time. We find that complete evaporation time of an inclined droplet becomes longer as gravitational influence by inclination become… Show more
“…While directly relevant, the reported measurements of Kim et al . 25 appear to contain inconsistencies, which makes it challenging to use them for comparison. For instance, it is not immediately clear why the contact radius changes linearly with time at a constant contact angle on a horizontal substrate.…”
Section: Resultsmentioning
confidence: 99%
“…Lastly, Kim et al . 25 experimentally measured the lifetime and evaporation dynamics of water droplets on slopes of various tilt angles. Overall, a close inspection of the literature indicates that our theoretical understanding of the effect of gravity on the evaporation of droplets sitting on tilted substrates is incomplete.…”
We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from the purely diffusive transport of liquid vapor and that the contact line is a pinned circle. For the purposes of the analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the droplet is unperturbed by the effect of gravity and takes the form of a spherical cap, for which the vapor concentration field is already known. Here, the Young-Laplace equation is solved analytically to calculate the first-order correction to the shape of the drop. Knowing the first-order perturbation to the drop geometry and the zeroth-order distribution of vapor concentration, we obtain the leading-order contribution of gravity to the rate of droplet evaporation by utilizing Green’s second identity. The analytical results are supplemented by numerical calculations, where the droplet shape is first determined by minimizing the Helmholtz free energy and then the evaporation rate is computed by solving Laplace’s equation for the vapor concentration field via a finite-volume method. Perhaps counter-intuitively, we find that even when the droplet deforms noticeably under the influence of gravity, the rate of evaporation remains almost unchanged, as if no gravitational effect is present. Furthermore, comparison between analytical and numerical calculations reveals that considering only the leading-order corrections to the shape of the droplet and vapor concentration distribution provides estimates that are valid well beyond their intended limit of very small Bo.
“…While directly relevant, the reported measurements of Kim et al . 25 appear to contain inconsistencies, which makes it challenging to use them for comparison. For instance, it is not immediately clear why the contact radius changes linearly with time at a constant contact angle on a horizontal substrate.…”
Section: Resultsmentioning
confidence: 99%
“…Lastly, Kim et al . 25 experimentally measured the lifetime and evaporation dynamics of water droplets on slopes of various tilt angles. Overall, a close inspection of the literature indicates that our theoretical understanding of the effect of gravity on the evaporation of droplets sitting on tilted substrates is incomplete.…”
We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from the purely diffusive transport of liquid vapor and that the contact line is a pinned circle. For the purposes of the analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the droplet is unperturbed by the effect of gravity and takes the form of a spherical cap, for which the vapor concentration field is already known. Here, the Young-Laplace equation is solved analytically to calculate the first-order correction to the shape of the drop. Knowing the first-order perturbation to the drop geometry and the zeroth-order distribution of vapor concentration, we obtain the leading-order contribution of gravity to the rate of droplet evaporation by utilizing Green’s second identity. The analytical results are supplemented by numerical calculations, where the droplet shape is first determined by minimizing the Helmholtz free energy and then the evaporation rate is computed by solving Laplace’s equation for the vapor concentration field via a finite-volume method. Perhaps counter-intuitively, we find that even when the droplet deforms noticeably under the influence of gravity, the rate of evaporation remains almost unchanged, as if no gravitational effect is present. Furthermore, comparison between analytical and numerical calculations reveals that considering only the leading-order corrections to the shape of the droplet and vapor concentration distribution provides estimates that are valid well beyond their intended limit of very small Bo.
“…After the contact line of a liquid droplet is depinned on a solid substrate, the sliding motion is often confirmed 27 . However, such a sliding motion was never observed in our system, suggesting that the movement of the SLG boundary toward the droplet center is not such a sliding motion.…”
Inkjet printing is of growing interest due to the attractive technologies for surface patterning. During the printing process, the solutes are transported to the droplet periphery and form a ring-like deposit, which disturbs the fabrication of high-resolution patterns. Thus, controlling the uniformity of particle coating is crucial in the advanced and extensive applications. Here, we find that sweet coffee drops above a threshold sugar concentration leave uniform rather than the ring-like pattern. The evaporative deposit changes from a ring-like pattern to a uniform pattern with an increase in sugar concentration. We moreover observe the particle movements near the contact line during the evaporation, suggesting that the sugar is precipitated from the droplet edge because of the highest evaporation and it causes the depinning of the contact line. By analyzing the following dynamics of the depinning contact line and flow fields and observing the internal structure of the deposit with a FIB-SEM system, we conclude that the depinned contact line recedes due to the solidification of sugar solution without any slip motion while suppressing the capillary flow and homogeneously fixing suspended particles, leading to the uniform coating. Our findings show that suppressing the coffee-ring effect by adding sugar is a cost-effective, easy and nontoxic strategy for improving the pattern resolution.
“…This confirms the negligible effect of the evaporation rate in the range 2 s < t < 6 s for on evaluation of ECA for our tests. During the “evaporation” stage, the evaporation is influenced by the DCA 5 , 32 , 33 . Figure 2 IR-camera images of a sessile water drop deposed on a hot aluminium surface.…”
The measurement of the equilibrium contact angle (ECA) of a weakly evaporating sessile drop becomes very challenging when the temperatures are higher than ambient temperature. Since the ECA is a critical input parameter for numerical simulations of diabatic processes, it is relevant to know the variation of the ECA with the fluid and wall temperatures. Several research groups have studied the effect of temperature on ECA either experimentally, with direct measures, or numerically, using molecular dynamic simulations. However, there is some disagreement between the authors. In this paper two possible theoretical models are presented, describing how the ECA varies with the surface temperature. These two models (called Decreasing Trend Model and Unsymmetrical Trend Model, respectively) are compared with experimental measurements. Within the experimental errors, the equilibrium contact angle shows a decrease with increasing surface temperatures on the hydrophilic surface. Conversely the ECA appears approximately constant on hydrophobic surfaces for increasing wall temperatures. The two conclusions for practical applications for weakly evaporating conditions are that (i) the higher the ECA, the smaller is the effect of the surface temperature, (ii) a good evaluation of the decrease of the ECA with the surface temperature can be obtained by the proposed DTM approach.
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