Coalescence-induced jumping of droplet: Inertia and viscosity effects

The problem of coalescence-induced self-propelled jumping of droplet is studied using three-dimensional numerical simulation. The focus is on the effect of inertia and in particular the effect of air density on the behavior of the merged droplet during jumping. A lattice Boltzmann method is used for two identical, static micro-droplets coalescing on a homogeneous substrate with contact angle ranging from 0∘ to 180∘. The results reveal that the effect of air density is significant on detachment of the merged droplet from the substrate at the later stage of the jumping process; the larger the air density, the larger the jumping height of the droplet. Analysis of streamlines and vorticity contours is performed for density ratios ranging from 60 to 800. These show a generation of vortical structures inside and around the droplet. The intensity of these structures gets weaker after droplet departure as the air inertia is decreased. The results are also presented in terms of phase diagrams of the merged droplet jumping for different Ohnesorge numbers (Oh) and surface wettabilities for both small and large density ratios. The critical value of contact angle where the merged droplet jumps away from the substrate is independent of density ratio and has a value around 150∘. However, the critical value of Oh depends on both density ratio and wettability of the surface for contact angles greater than 150∘. In this range of contact angle, the diagrams show two distinct dynamical regimes for different density ratios, namely, inertial and viscous regimes.

[1]  John W. Cahn,et al.  Critical point wetting , 1977 .

[2]  P. Collier,et al.  Delayed frost growth on jumping-drop superhydrophobic surfaces. , 2013, ACS nano.

[3]  Zhong Lan,et al.  Analysis of droplet jumping phenomenon with lattice Boltzmann simulation of droplet coalescence , 2013 .

[4]  Lin Liu,et al.  Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces , 2010, J. Comput. Phys..

[5]  Ya-Pu Zhao,et al.  Size effect on the coalescence-induced self-propelled droplet , 2011 .

[6]  Yue-Hong Qian,et al.  Dissipative and dispersive behaviors of lattice-based models for hydrodynamics , 2000 .

[7]  Jolanta A Watson,et al.  Self-cleaning of superhydrophobic surfaces by self-propelled jumping condensate , 2013, Proceedings of the National Academy of Sciences.

[8]  Shuhuai Yao,et al.  Why condensate drops can spontaneously move away on some superhydrophobic surfaces but not on others. , 2012, ACS applied materials & interfaces.

[9]  Jiangtao Cheng,et al.  Condensation heat transfer on two-tier superhydrophobic surfaces , 2012 .

[10]  Yuejun Zhao,et al.  Planar Jumping-Drop Thermal Diodes , 2011 .

[11]  James J. Feng,et al.  Numerical simulations of self-propelled jumping upon drop coalescence on non-wetting surfaces , 2014, Journal of Fluid Mechanics.

[12]  Taehun Lee,et al.  WALL FREE ENERGY BASED POLYNOMIAL BOUNDARY CONDITIONS FOR NON-IDEAL GAS LATTICE BOLTZMANN EQUATION , 2008 .

[13]  Yeomans,et al.  Lattice Boltzmann simulations of liquid-gas and binary fluid systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  J. Boreyko,et al.  Self-propelled dropwise condensate on superhydrophobic surfaces. , 2009, Physical review letters.

[15]  D. Jacqmin Regular Article: Calculation of Two-Phase Navier–Stokes Flows Using Phase-Field Modeling , 1999 .

[16]  J. Koplik,et al.  Multiscale liquid drop impact on wettable and textured surfaces , 2013 .

[17]  Michael A. Nilsson,et al.  The effect of contact angle hysteresis on droplet coalescence and mixing. , 2011, Journal of colloid and interface science.

[18]  Carsten Werner,et al.  Smart Skin Patterns Protect Springtails , 2011, PloS one.

[19]  Yoshiaki Oka,et al.  Two-dimensional simulation of drop deformation and breakup at around the critical Weber number , 2003 .

[20]  Evelyn N Wang,et al.  Jumping-droplet-enhanced condensation on scalable superhydrophobic nanostructured surfaces. , 2012, Nano letters.

[21]  J. Chen,et al.  Anti-icing surfaces based on enhanced self-propelled jumping of condensed water microdroplets. , 2013, Chemical communications.

[22]  M. Tiwari,et al.  Flow condensation on copper-based nanotextured superhydrophobic surfaces. , 2013, Langmuir : the ACS journal of surfaces and colloids.

[23]  S. Zaleski,et al.  Coalescence of liquid drops by surface tension. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Wei Sun,et al.  Mechanism study of condensed drops jumping on super-hydrophobic surfaces , 2012 .

[25]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Jolanta A Watson,et al.  A dual layer hair array of the brown lacewing: repelling water at different length scales. , 2011, Biophysical journal.

[27]  Xiaojun Quan,et al.  Lattice Boltzmann simulations for self-propelled jumping of droplets after coalescence on a superhydrophobic surface , 2014 .

[28]  Seungwon Shin,et al.  Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity , 2002 .

[29]  Samaneh Farokhirad,et al.  Effects of Inertia and Viscosity on Single Droplet Deformation in Confined Shear Flow , 2013 .

[30]  Andrei G. Fedorov,et al.  Visualization of droplet departure on a superhydrophobic surface and implications to heat transfer enhancement during dropwise condensation , 2010 .

[31]  Di Gao,et al.  Anti-icing superhydrophobic coatings. , 2009, Langmuir : the ACS journal of surfaces and colloids.

[32]  Taehun Lee,et al.  Effects of initial conditions on the simulation of inertial coalescence of two drops , 2014, Comput. Math. Appl..

[33]  Chunfeng Zhou,et al.  Sharp-interface limit of the Cahn–Hilliard model for moving contact lines , 2010, Journal of Fluid Mechanics.

[34]  D. d'Humières,et al.  Multiple–relaxation–time lattice Boltzmann models in three dimensions , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[35]  Robert Forchheimer,et al.  Rebounding Droplet‐Droplet Collisions on Superhydrophobic Surfaces: from the Phenomenon to Droplet Logic , 2012, Advanced materials.

[36]  Konrad Rykaczewski,et al.  Microdroplet growth mechanism during water condensation on superhydrophobic surfaces. , 2012, Langmuir : the ACS journal of surfaces and colloids.

[37]  Seungwon Shin,et al.  Energy and hydrodynamic analyses of coalescence-induced jumping droplets , 2013 .

[38]  Taehun Lee,et al.  Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids , 2009, Comput. Math. Appl..

[39]  Xuemei Chen,et al.  Multimode multidrop serial coalescence effects during condensation on hierarchical superhydrophobic surfaces. , 2013, Langmuir : the ACS journal of surfaces and colloids.