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Understanding the evaporation and imbibition of surfactant-laden droplets on porous media is both scientifically challenging and industrially important, such as in inkjet printing applications. In inkjet printing, a uniform ink deposition pattern and prevention of droplet coalescence are desirable for high print quality. The addition of surfactants can alter the surface tension at the liquid–gas interface of droplets [1,2], suppress coffee-ring effects, and induce a more uniform ink deposition pattern. Surfactants can also change interfacial energies within porous media, possibly accelerating droplet penetration into the porous medium and hence preventing droplet coalescence [3,4]. As a result, surfactants are widely used in inkjet-printed droplets.
It is commonly assumed that imbibition occurs much faster than droplet evaporation in inkjet printing processes [5]. However, some experimental and numerical studies showed that evaporation may dominate, compete with, or be negligible compared with the imbibition of inkjet-printed droplets [6,7], depending on parameters such as droplet size, ambient relative humidity, temperature, pore diameter, and substrate porosity, etc. The effects of surfactants on droplet flow and imbibition dynamics in porous media may differ between evaporation-dominated and imbibition-dominated processes, due to differences in surfactant concentration distributions under these conditions. Therefore, understanding the effects of surfactants on simultaneous evaporation and imbibition is significant for optimizing inkjet printing performance.
The evaporation of surfactant-laden droplets on thin porous media is a complex process that includes droplet evaporation, droplet imbibition into unsaturated porous media, and surfactant transport within both the droplet and the porous medium. These coupled processes are illustrated schematically in Figure 1. In this work, we use numerical methods to investigate these coupled process for surfactant-laden droplets on porous media. Droplet flow is described using lubrication theory under the assumption of small droplet-substrate contact angles, including an analytical evaporation flux and an imbibition flux into the porous medium. Droplet imbibition in the porous medium is modeled using the Richards equation to describe unsaturated flow, which was found in paper-based porous materials [8]. Surfactant transport is modeled using a mass-conservative convection–diffusion–adsorption model, including adsorption at the droplet–air interface as well as liquid–solid and liquid–gas interfaces within the porous medium. The evolution of the liquid–gas interfacial area in porous media is calculated using a thermodynamic approach [9,10] that considers surfactant-induced area changes.
We study two-dimensional axisymmetric problems in cylindrical coordinates, incorporating both evaporation and imbibition in unsaturated porous media for droplets of typical inkjet printing size. The effects of liquid-gas interfacial adsorption in porous media on imbibition dynamics are analyzed. In particular, we study regimes in which evaporation dominates, competes with, or is negligible relative to imbibition, and investigate how surfactants affect the flow patterns in the droplet and imbibition dynamics into the porous medium under these conditions.
| References | [1] Van Gaalen, R. T., et al. "The evaporation of surfactant-laden droplets: A comparison between contact line models." Journal of colloid and interface science 579 (2020): 888-897. [2] Van Gaalen, R. T., et al. "Marangoni circulation in evaporating droplets in the presence of soluble surfactants." Journal of colloid and interface science 584 (2021): 622-633. [3] Daniel, R. C., & Berg, J. C. (2006). Spreading on and penetration into thin, permeable print media: Application to ink-jet printing. Advances in colloid and interface science, 123, 439-469. [4] Van Gaalen, R. T., Diddens, C., Siregar, D. P., Wijshoff, H. M. A., & Kuerten, J. G. M. (2021). Absorption of surfactant-laden droplets into porous media: A numerical study. Journal of colloid and interface science, 597, 149-159. [5] Tan, H. (2017). Absorption of picoliter droplets by thin porous substrates. AIChE Journal, 63(5), 1690-1703. [6] Oko, A., Swerin, A., & Claesson, P. M. (2011). Imbibition and evaporation of water droplets on paper and solid substrates. Journal of Imaging Science and Technology, 55(1), 010201. [7] Pham, T., & Kumar, S. (2019). Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates. Physical Review Fluids, 4(3), 034004. [8] Nicasy, R., Huinink, H. P., Erich, S. J. F., & Adan, O. C. G. (2021). High-speed NMR imaging of capillary action in thin nontransparent porous media. Physical Review E, 104(4), L043101. [9] Leverett, M. (1941). Capillary behavior in porous solids. Transactions of the AIME, 142(01), 152-169. [10] Brusseau, Mark L., and Bo Guo. "Air-water interfacial areas relevant for transport of per and poly-fluoroalkyl substances." Water research 207 (2021): 117785. |
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| Country | Netherlands |
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