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. 2021 Mar 15;12:1673. doi: 10.1038/s41467-021-21832-x

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — a Illustration for the Marangoni effect. F_M is the force induced by Marangoni stresses, while F_D is the viscous drag force. γ_L and γ₀ is the interfacial tension between PEG-rich and DEX-rich phase with or without the presence of liposomes. b The total intensity of liposome coating and corresponding droplet velocity (U) for different droplets. c The relationship between maximum velocity (U_max) and droplet diameter (D). The difference in the slope for different batches is due to the variations in polymer gradients. d The relationship between normalised velocity (U_R, the ratio of droplet velocity at different time points to its maximum velocity) and the value of ε (h/D). 20 droplets from four trials were chosen for analysis. e Chasing and merge process for two droplets with different diameter. Pictures were extracted from Supplementary Movie 6 and cropped for better presentation. Scale bar is 50 μm.