An Electromechanical Model for Electrowetting With Finite Droplet Size

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Deng Huang ◽  
Fang Qian ◽  
Wenyao Zhang ◽  
Wenbo Li ◽  
Rui Chuan ◽  
...  
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Finite Size ◽  
Surface Tension Force ◽  
Equilibrium Contact Angle ◽  
Electric Force ◽  
Electromechanical Model ◽  
Flat Substrate ◽  
Three Phase ◽  
Maxwell Stresses

Abstract We present an electromechanical model for the analysis of electrowetting by considering the balance between an electric force and a surface tension force acting on the contact line of three phases, namely the droplet (D) phase, the substrate (S) phase, and the ambiance (A) phase. We show that the Maxwell stresses at the ambiance–substrate (A–S) interface, the droplet–substrate (D–S) interface, and the droplet–ambiance (D–A) interface induce an electric force on the three-phase contact line which is responsible for the modification of the apparent contact angle in electrowetting. For a classical electrowetting configuration with a flat substrate, we show that the electric force on the contact line (or the electrowetting number) is mainly due to the Maxwell stresses at the D–A interface. The model is validated by its excellent agreement with the classical Young-Lippmann (Y-L) model for sufficiently large droplets and comparable electric permittivities between A and S phases. Interestingly, our new model reveals that the finite size of droplet produces profound effects on the electrowetting that the electrowetting number becomes dependent on the permittivity of A phase and the equilibrium contact angle, which is in stark contrast to the Y-L model. The reasons for these remarkable effects are elaborated and clarified. The findings in the current study are complementary to the classical Y-L model and provide new insights into the electrowetting phenomenon.

An Electromechanical Model for Electrowetting

2019 ◽  
Author(s):  
Deng Huang ◽  
Fang Qian ◽  
Wenyao Zhang ◽  
Cunlu Zhao ◽  
Wenbo Li ◽  
...  
Keyword(s):  
Contact Angle ◽  
Droplet Size ◽  
Contact Line ◽  
Surface Tension Force ◽  
S Phase ◽  
Electric Force ◽  
Electromechanical Model ◽  
Three Phase ◽  
The Difference ◽  
Maxwell Stresses

Abstract We present an electromechanical model for analysis of electrowetting by considering the balance between an electric force and a surface tension force acting on the contact line of three phases, namely the droplet (D) phase the substrate (S) phase and the ambiance (A) phase. We show that the electric force acting on the three-phase contact line generally is contributed by the Maxwell stresses at the ambiance-substrate (A-S) interface, the droplet-substrate (D-S) interface, and the droplet-ambiance (D-A) interface. It was identified that the change of contact angle in electrowetting is essentially a consequence of the modification of the electric force on the contact line. For a classical electrowetting configuration, we show that the electric force on the contact line is mainly due to the Maxwell stresses at the D-A interface. Then we examine comprehensively how the electric force on the contact line varies with the permittivity difference between A and S phases, the contact angle and size. It was found that our model agrees excellently with the classical Yong-Lippmann (Y-L) model when the permittivities of A and S phases are equal, while the difference between the two increases as the permittivity difference between A and S phases increases. The electric force increases with the increase of the contact angle for a given droplet size. Our model approaches the Y-L model with the increasing droplet size. The findings are complementary to the classical Y-L model and provide new insights into the electrowetting.

Surface Topography Induced Ultrahydrophobic Behavior: Effect of Three-Phase Contact Line Topology

2006 ◽  
Author(s):  
Neeharika Anantharaju ◽  
Mahesh Panchagnula ◽  
Wayne Kimsey ◽  
Sudhakar Neti ◽  
Svetlana Tatic-Lucic
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Anomalous Behavior ◽  
Contact Angles ◽  
Wet Etching ◽  
Surface Geometry ◽  
Wetting Behavior ◽  
Void Fractions ◽  
Three Phase ◽  
Receding Contact

The wettability of silicon surface hydrophobized using silanization reagents was studied. The advancing and receding contact angles were measured with the captive needle approach. In this approach, a drop under study was held on the hydrophobized surface with a fine needle immersed in it. The asymptotic advancing and receding angles were obtained by incrementally increasing the volume added and removed, respectively, until no change in angles was observed. The values were compared with the previously published results. Further, the wetting behavior of water droplets on periodically structured hydrophobic surfaces was investigated. The surfaces were prepared with the wet etching process and contain posts and holes of different sizes and void fractions. The surface geometry brought up a scope to study the Wenzel (filling of surface grooves) and Cassie (non filling of the surface grooves) theories and effects of surface geometry and roughness on the contact angle. Experimental data point to an anomalous behavior where the data does not obey either Wenzel or Cassie type phenomenology. This behavior is explained by an understanding of the contact line topography. The effect of contact line topography on the contact angle was thus parametrically studied. It was also inferred that, the contact angle increased with the increase in void fraction. The observations may serve as guidelines in designing surfaces with the desired wetting behavior.

scholarly journals Deformation of an elastic substrate due to a resting sessile droplet

2017 ◽  
Vol 29 (2) ◽  
pp. 281-300 ◽  
Author(s):  
AARON BARDALL ◽  
KAREN E. DANIELS ◽  
MICHAEL SHEARER
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Substrate Surface ◽  
Fluid Pressure ◽  
Force Balance ◽  
Energy Conditions ◽  
Equilibrium Contact Angle ◽  
Solution Technique ◽  
Vertical Force ◽  
Tangential Contact

On a sufficiently soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates that deform under loading. It remains an open question whether the contact line transmits a non-zero force tangent to the substrate surface in addition to the conventional normal (vertical) force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions, which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a non-zero tangential contact line force, it is necessary to include a previously neglected horizontal traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero tangential contact line forces.

scholarly journals MODELLING AND INVESTIGATION OF THE DEPENDENCE OF SUPERHYDROPHOBIC PROPERTIES OF NANOSURFACES ON THE TOPOLOGY OF MICROCHANNELS

2019 ◽  
Vol 3 ◽  
pp. 52
Author(s):  
Sharif E. Guseynov ◽  
Jekaterina V. Aleksejeva
Keyword(s):  
Contact Angle ◽  
Interphase Boundary ◽  
Slip Length ◽  
Superhydrophobic Surfaces ◽  
Equilibrium Contact Angle ◽  
Three Phase ◽  
Quantitative Understanding ◽  
Air Cushion ◽  
Local Slip ◽  
Solid Liquid

In the Cassie-Baxter state anisotropic superhydrophobic surfaces have high lubricating properties. Such superhydrophobic surfaces are used in medical implants, aircraft industry, vortex bioreactors etc. In spite of the fact that quantitative understanding of fluid dynamics on anisotropic superhydrophobic surfaces has been broadened substantially for last several years, there still are some unsolved problems in this field. This work investigates dynamics of a liquid on unidirectional superhydrophobic surfaces in the Cassie-Baxter state, when surface texture is filled with gas and, consequently, the liquid virtually is located on some kind of an air cushion. Energy of the interphase boundary liquid-gas is much smaller than energy of the interphase boundary solid-liquid, that is why the contact angle at wetting such surfaces differs a lot from the Young contact angle and depends on contact area ratio of liquid-gas and liquid-solid in visible contact of liquid and surface. Considering difference in energy obtained if we slightly shift the three-phase contact line, expression for macroscopic equilibrium contact angle, which describes the Cassie-Baxter state, can be deduced. In the work the design formula for computing local-slip length profiles of liquid on the considered superhydrophobic surfaces is obtained.

scholarly journals Dynamics of droplets under electrowetting effect with voltages exceeding the contact angle saturation threshold

2021 ◽  
Vol 925 ◽  
Author(s):  
Quoc Vo ◽  
Tuan Tran
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Applied Voltage ◽  
Droplet Surface ◽  
Capillary Waves ◽  
Force Balance ◽  
Equilibrium Contact Angle ◽  
Initial Contact ◽  
Viscous Effects ◽  
Electrowetting On Dielectric

Electrowetting on dielectric (EWOD) is a powerful tool in many droplet-manipulation applications with a notorious weakness caused by contact-angle saturation (CAS), a phenomenon limiting the equilibrium contact angle of an EWOD-actuated droplet at high applied voltage. In this paper, we study the spreading behaviours of droplets on EWOD substrates with the range of applied voltage exceeding the saturation limit. We experimentally find that at the initial stage of spreading, the driving force at the contact line still follows the Young–Lippmann law even if the applied voltage is higher than the CAS voltage. We then theoretically establish the relation between the initial contact-line velocity and the applied voltage using the force balance at the contact line. We also find that the amplitude of capillary waves on the droplet surface generated by the contact line's initial motion increases with the applied voltage. We provide a working framework utilising EWOD with voltages beyond CAS by characterising the capillary waves formed on the droplet surface and their self-similar behaviours. We finally propose a theoretical model of the wave profiles taking into account the viscous effects and verify this model experimentally. Our results provide avenues to utilise the EWOD effect with voltages beyond the CAS threshold, and have strong bearing on emerging applications such as digital microfluidic and ink-jet printing.

scholarly journals Wetting of doubly periodic rough surfaces in Wenzel’s regime

2018 ◽  
Vol 145 ◽  
pp. 03006
Author(s):  
Stanimir Iliev ◽  
Nina Pesheva ◽  
Pavel Iliev
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Numerical Study ◽  
Rough Surfaces ◽  
Contact Angle Hysteresis ◽  
Stick Slip ◽  
Liquid Meniscus ◽  
Three Phase ◽  
Mutual Disposition ◽  
Physical Defects

In this work we present preliminary results from our numerical study of the shapes of a liquid meniscus in contact with doubly sinusoidal rough surfaces in Wenzel’s wetting regime. Using the full capillary model we obtain the advancing and the receding equilibrium meniscus shapes for a broad interval of surface roughness factors. The contact angle hysteresis is obtained when the three-phase contact line is located on one row (block case) or several rows (kink case) of physical defects. We find that depending on the mutual disposition of the contact line and the lattice of periodic defects, different stick-slip behaviors of the contact line depinning mechanism appear, leading to different values of the contact angle hysteresis.

Moving contact lines in liquid/liquid/solid systems

1997 ◽  
Vol 334 ◽  
pp. 211-249 ◽  
Author(s):  
YULII D. SHIKHMURZAEV
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Contact Angle ◽  
Flow Field ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Three Phase

A general mathematical model which describes the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface is examined in the case of small capillary and Reynolds numbers. The model stems from a conclusion that the Young equation, σ1 cos θ = σ2 − σ3, which expresses the balance of tangential projection of the forces acting on the three-phase contact line in terms of the surface tensions σi and the contact angle θ, together with the well-established experimental fact that the dynamic contact angle deviates from the static one, imply that the surface tensions of contacting interfaces in the immediate vicinity of the contact line deviate from their equilibrium values when the contact line is moving. The same conclusion also follows from the experimentally observed kinematics of the flow, which indicates that liquid particles belonging to interfaces traverse the three-phase interaction zone (i.e. the ‘contact line’) in a finite time and become elements of another interface – hence their surface properties have to relax to new equilibrium values giving rise to the surface tension gradients in the neighbourhood of the moving contact line. The kinematic picture of the flow also suggests that the contact-line motion is only a particular case of a more general phenomenon – the process of interface formation or disappearance – and the corresponding mathematical model should be derived from first principles for this general process and then applied to wetting as well as to other relevant flows. In the present paper, the simplest theory which uses this approach is formulated and applied to the moving contact-line problem. The model describes the true kinematics of the flow so that it allows for the ‘splitting’ of the free surface at the contact line, the appearance of the surface tension gradients near the contact line and their influence upon the contact angle and the flow field. An analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived and examined. The role of a ‘thin’ microscopic residual film formed by adsorbed molecules of the receding fluid is considered. The flow field in the vicinity of the contact line is analysed. The results are compared with experimental data obtained for different fluid/liquid/solid systems.

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