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C: Surfaces, Interfaces, Porous Materials, and Catalysis
The Maximum Spreading Factor for Polymer Nanodroplets Impacting a Hydrophobic Solid Surface Yi-Bo Wang, Xiao-Dong Wang, Yan-Ru Yang, and Min Chen J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b02053 • Publication Date (Web): 06 May 2019 Downloaded from http://pubs.acs.org on May 6, 2019
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The Journal of Physical Chemistry
The Maximum Spreading Factor for Polymer Nanodroplets Impacting a Hydrophobic Solid Surface
Yi-Bo Wang1,2,3, Xiao-Dong Wang1,2,3*, Yan-Ru Yang1,2,3, Min Chen4** 1. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China; 2. Research Center of Engineering Thermophysics, North China Electric Power University, Beijing 102206, China; 3. Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Education, North China Electric Power University, Beijing 102206, China; 4. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
Abstract: In this work, we investigate the impact behaviors of nanoscale polymer droplets on a solid surface via molecular dynamics (MD) simulations. The maximum spreading factor is focused on understanding the energy dissipation mechanism during impact. Our simulations show that the macroscale model for blood droplets and the nanoscale models for water droplets cannot capture the simulated maximum spreading factor of nanoscale polymer droplets. We demonstrate that viscous dissipation for nanoscale polymer droplets stems from the velocity gradients in both the impact and the spreading direction; whereas for macroscale blood droplets and nanoscale water droplets, only the velocity gradient in the impact direction contributes to it. With the consideration of different dissipation mechanism, we propose a modified expression of viscous dissipation and develop a new 1
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model to predict the maximum spreading factor of nanoscale polymer droplets. By comparing the model predictions with MD simulations, we show that the new model can capture more precisely the simulated maximum spreading factor for nanoscale polymer droplets with chain length ranging from 40 to 100. The present simulations and developed model can provide useful insights into the mechanism of nanoscale polymer droplets impacting surfaces.
*Corresponding Author: Xiao-Dong Wang, Tel. and Fax: +86-10-62321277, E-mail address:
[email protected] **Corresponding Author: Min Chen, Tel. and Fax: +86-10-62797062, E-mail address:
[email protected] 2
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The Journal of Physical Chemistry
■ INTRODUCTION Impact of droplets on solid surfaces is commonly encountered in nature, e.g., an ink blot or a coffee stain. However, the problem associated with droplets impacting surfaces had puzzled scientists for over a century.1 Various outcomes can be observed when a droplet impacts surfaces, such as spreading, sticking, recoil, splashing, and rebound. The challenge of understanding impact dynamics arises from its complicated physical process which is controlled by several forces, including the inertial force, capillary force, viscous force, and gravitational force. In the absence of splashing, a maximum spreading diameter will be reached when the droplet spreads over the surface, which is one of the most important parameters of interest in many applications, such as inkjet printing,2 spray cooling,3 forensic science,4 and so forth. For example, the quality of high resolution in inkjet printing is directly related to the area wetted by impacting droplets on the printed surface after deposition.5 For the forensic application, the maximum spreading diameter is also crucial for bloodstain pattern analysis to determine the accurate position of a victim.6 The ability to precisely predict the maximum spreading diameter is fundamental to optimizing processes in these applications. The maximum spreading diameter, Dmax, is commonly normalized by the initial droplet diameter D0, defined as the maximum spreading factor, βmax=Dmax/D0. Understanding the mechanism behind the maximum spreading factor is still a challenging task, because the factor is affected by several forces mentioned above. In general, these forces are quantified in terms of dimensionless numbers: Weber number, We=ρD0Vimp2/γ, defined as the ratio of inertial and capillary forces, Reynolds number, Re=ρD0Vimp/μ, the ratio of inertial and viscous forces, 3
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Ohnesorge number, Oh=μ/(ρD0γ)1/2, the ratio of viscous and inertial-capillary forces, Capillary number, Ca=μVimp/γ, the ratio of the viscous and capillary forces, and Froude number, Fr=Vimp/(gD0)1/2, the ratio of inertial and gravitational forces. Here, ρ is the liquid density, Vimp is the impact velocity, γ is the surface tension of the liquid, μ is the liquid viscosity, and g is the gravitational acceleration. For usual impact conditions, the inertial force is much larger than the gravitational force, so that the gravitational force can be safely neglected.7 Two asymptotic impact regimes have been extensively investigated.8-12 One is the capillary regime where viscous force is negligibly small, and the other is the viscous regime where capillary force is negligibly small. An impact parameter P=WeRe-4/5 is commonly used to distinguish the two regimes with P>>1 denoting the viscous regime and P
