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Lei Y, Liu B, Zhuang L, Guo Y, Sun H, Yuan D, Tang B, Liu F, Zhou G. Accurate and Wide-Voltage-Range Modeling of Electrowetting with a Lattice Boltzmann Approach. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:12110-12123. [PMID: 37596256 DOI: 10.1021/acs.langmuir.3c01395] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/20/2023]
Abstract
The lattice Boltzmann method (LBM) has been widely used in multi-phase fluid mechanics and is known to be more computationally efficient than the traditional method of numerically solving Navier-Stokes and Cahn-Hilliard equations. Electrowetting is an important component of interfacial sciences, in which the liquid-liquid and solid-liquid interfaces are tuned by electrostatics. Modeling electrowetting using the LBM can be categorized into surface and bulk methods. By modifying the surface tension scalar, the surface method easily reproduces the fundamental Young-Lippmann (YL) equation at low voltages but fails to capture contact angle saturation at high voltages. With fully coupled hydrodynamics and electrostatics in the form of spatially dependent matrices, the bulk method can successfully show contact angle saturation, but it is often unable to reproduce the YL equation due to its intrinsic inaccuracies. The inaccuracies are mainly due to the fact that while the hydrodynamics are all described by continuous physical quantities in the framework of diffusive interfaces, the interfacial electrostatics are governed by discontinuous electric fields caused by sheet charge density. In this paper, we show that accurately modeling electrowetting using the LBM is non-trivial. Additional modeling work, especially the treatment of interfacial electric fields, is needed to recover the fundamental YL equation at low voltages and predict contact angle saturation at high voltages, with a systematic model validation over key parameters and applications.
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Affiliation(s)
- Yongxin Lei
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Bin Liu
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Lei Zhuang
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Yuanyuan Guo
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Hailing Sun
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Dong Yuan
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Biao Tang
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Feilong Liu
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
| | - Guofu Zhou
- Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, P. R. China
- Shenzhen Guohua Optoelectronics Tech. Co. Ltd., Shenzhen 518110, P. R. China
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Xu X, Wang F, Qin Z, Wen B. Electrowetting lattice Boltzmann method for micro- and nano-droplet manipulations. Phys Rev E 2023; 107:045305. [PMID: 37198769 DOI: 10.1103/physreve.107.045305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2022] [Accepted: 03/23/2023] [Indexed: 05/19/2023]
Abstract
Electrowetting has become a widely used tool for manipulating tiny amounts of liquids on surfaces. This paper proposes an electrowetting lattice Boltzmann method for manipulating micro-nano droplets. The hydrodynamics with the nonideal effect is modeled by the chemical-potential multiphase model, in which the phase transition and equilibrium are directly driven by chemical potential. For electrostatics, droplets in the micro-nano scale cannot be considered as equipotential as macroscopic droplets due to the Debye screening effect. Therefore, we linearly discretize the continuous Poisson-Boltzmann equation in a Cartesian coordinate system, and the electric potential distribution is stabilized by iterative computations. The electric potential distribution of droplets at different scales suggests that the electric field can still penetrate micro-nano droplets even with the screening effect. The accuracy of the numerical method is verified by simulating the static equilibrium of the droplet under the applied voltage, and the results show the apparent contact angles agree very well with the Lippmann-Young equation. The microscopic contact angles present some obvious deviations due to the sharp decrease of electric field strength near the three-phase contact point. These are consistent with previously reported experimental and theoretical analyses. Then, the droplet migrations on different electrode structures are simulated, and the results show that droplet speed can be stabilized more quickly due to the more uniform force on the droplet in the closed symmetric electrode structure. Finally, the electrowetting multiphase model is applied to study the lateral rebound of droplets impacting on the electrically heterogeneous surface. The electrostatic force prevents the droplets from contracting on the side which is applied voltage, resulting in the lateral rebound and transport toward the side.
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Affiliation(s)
- Xin Xu
- Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education, Guangxi Normal University, Guilin 541004, China and Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin 541004, China
| | - Fei Wang
- Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education, Guangxi Normal University, Guilin 541004, China and Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin 541004, China
| | - Zhangrong Qin
- Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education, Guangxi Normal University, Guilin 541004, China and Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin 541004, China
| | - Binghai Wen
- Key Lab of Education Blockchain and Intelligent Technology, Ministry of Education, Guangxi Normal University, Guilin 541004, China and Guangxi Key Lab of Multi-Source Information Mining and Security, Guangxi Normal University, Guilin 541004, China
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Ruiz-Gutiérrez É, Edwards AMJ, McHale G, Newton MI, Wells GG, Brown CV, Ledesma-Aguilar R. Lattice Boltzmann Simulations of Multiphase Dielectric Fluids. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:7328-7340. [PMID: 34101471 DOI: 10.1021/acs.langmuir.1c00606] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The dynamic effect of an electric field on dielectric liquids is called liquid dielectrophoresis. It is widely used in several industrial and scientific applications, including inkjet printing, microfabrication, and optical devices. Numerical simulations of liquid-dielectrophoresis are necessary to understand the fundamental physics of the phenomenon, but also to explore situations that might be difficult or expensive to implement experimentally. However, such modeling is challenging, as one needs to solve the electrostatic and fluid dynamics equations simultaneously. Here, we formulate a new lattice-Boltzmann method capable of modeling the dynamics of immiscible dielectric fluids coupled with electric fields within a single framework, thus eliminating the need of using separate algorithms to solve the electrostatic and fluid dynamics equations. We validate the numerical method by comparing it with analytical solutions and previously reported experimental results. Beyond the benchmarking of the method, we study the spreading of a droplet using a dielectrowetting setup and quantify the mechanism driving the variation of the apparent contact angle of the droplet with the applied voltage. Our method provides a useful tool to study liquid-dielectrophoresis and can be used to model dielectric fluids in general, such as liquid-liquid and liquid-gas systems.
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Affiliation(s)
- Élfego Ruiz-Gutiérrez
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Andrew M J Edwards
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Glen McHale
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Michael I Newton
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Gary G Wells
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
| | - Carl V Brown
- SOFT Group, School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, U.K
| | - Rodrigo Ledesma-Aguilar
- Institute for Multiscale Thermofluids, School of Engineering, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH9 3FB, U.K
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Armstrong S, McHale G, Ledesma-Aguilar R, Wells GG. Evaporation and Electrowetting of Sessile Droplets on Slippery Liquid-Like Surfaces and Slippery Liquid-Infused Porous Surfaces (SLIPS). LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:11332-11340. [PMID: 32882130 PMCID: PMC8011908 DOI: 10.1021/acs.langmuir.0c02020] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Sessile droplet evaporation underpins a wide range of applications from inkjet printing to coating. However, drying times can be variable and contact-line pinning often leads to undesirable effects, such as ring stain formation. Here, we show voltage programmable control of contact angles during evaporation on two pinning-free surfaces. We use an electrowetting-on-dielectric approach and Slippery Liquid-Infused Porous (SLIP) and Slippery Omniphobic Covalently Attached Liquid-Like (SOCAL) surfaces to achieve a constant contact angle mode of evaporation. We report evaporation sequences and droplet lifetimes across a broad range of contact angles from 105°-67°. The values of the contact angles during evaporation are consistent with expectations from electrowetting and the Young-Lippman equation. The droplet contact areas reduce linearly in time, and this provides estimates of diffusion coefficients close to the expected literature value. We further find that the total time of evaporation over the broad contact angle range studied is only weakly dependent on the value of the contact angle. We conclude that on these types of slippery surfaces, droplet lifetimes can be predicted and controlled by the droplet's volume and physical properties (density, diffusion coefficient, and vapor concentration difference to the vapor phase) largely independent of the precise value of contact angle. These results are relevant to applications, such as printing, spraying, coating, and other processes, where controlling droplet evaporation and drying is important.
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Affiliation(s)
- S. Armstrong
- Smart
Materials & Surfaces Laboratory, Faculty of Engineering &
Environment, Northumbria University, Newcastle upon Tyne, NE1
8ST, U.K.
- School
of Engineering, University of Edinburgh, Sanderson Building, Edinburgh, EH9 3FB, U.K.
| | - G. McHale
- Smart
Materials & Surfaces Laboratory, Faculty of Engineering &
Environment, Northumbria University, Newcastle upon Tyne, NE1
8ST, U.K.
- School
of Engineering, University of Edinburgh, Sanderson Building, Edinburgh, EH9 3FB, U.K.
| | - R. Ledesma-Aguilar
- Smart
Materials & Surfaces Laboratory, Faculty of Engineering &
Environment, Northumbria University, Newcastle upon Tyne, NE1
8ST, U.K.
- School
of Engineering, University of Edinburgh, Sanderson Building, Edinburgh, EH9 3FB, U.K.
| | - G. G. Wells
- Smart
Materials & Surfaces Laboratory, Faculty of Engineering &
Environment, Northumbria University, Newcastle upon Tyne, NE1
8ST, U.K.
- School
of Engineering, University of Edinburgh, Sanderson Building, Edinburgh, EH9 3FB, U.K.
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Baratian D, Ruiz-Gutiérrez É, Mugele F, Ledesma-Aguilar R. Slippery when wet: mobility regimes of confined drops in electrowetting. SOFT MATTER 2019; 15:7063-7070. [PMID: 31441482 DOI: 10.1039/c9sm01107b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The motion of confined droplets in immiscible liquid-liquid systems strongly depends on the intrinsic relative wettability of the liquids on the confining solid material and on the typical speed, which can induce the formation of a lubricating layer of the continuous phase. In electrowetting, which routinely makes use of aqueous drops in ambient non-polar fluids that wet the wall material, electric stresses enter the force balance in addition to capillary and viscous forces and confinement effects. Here, we study the mobility of droplets upon electrowetting actuation in a wedge-shaped channel, and the subsequent relaxation when the electrowetting actuation is removed. We find that the droplets display two different mobility regimes: a fast regime, corresponding to gliding on a thin film of the ambient fluid, and a slow regime, where the film is replaced by direct contact between the droplet and the channel walls. Using a combination of experiments and numerical simulations, we show that the cross-over between these regimes arises from the interplay between the small-scale dynamics of the thin film of ambient fluid and the large-scale motion of the droplet. Our results shed light on the complex dynamics of droplets in non-uniform channels driven by electric actuation, and can thus help the rational design of devices based on electrowetting-driven droplet transport.
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Affiliation(s)
- Davood Baratian
- Physics of Complex Fluids, MESA+ Institute for Nanotechnology, Department of Science and Technology, University of Twente, The Netherlands
| | - Élfego Ruiz-Gutiérrez
- Smart Materials and Surfaces Laboratory, Faculty of Engineering and Environment, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK.
| | - Frieder Mugele
- Physics of Complex Fluids, MESA+ Institute for Nanotechnology, Department of Science and Technology, University of Twente, The Netherlands
| | - Rodrigo Ledesma-Aguilar
- Smart Materials and Surfaces Laboratory, Faculty of Engineering and Environment, Northumbria University, Ellison Place, Newcastle upon Tyne NE1 8ST, UK.
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