Ratcheting Motion of Liquid Drops on Gradient Surfaces

Daniel, Susan; Sircar, Sanjoy; Gliem, Jill; Chaudhury, Manoj K.

doi:10.1021/la036221a

Cited by 202 publications

(227 citation statements)

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“…Theoretically, α V is a constant provided that the drag forces in the vicinity of the contact line scale with the fluid viscosity in the bulk region [22]. The relation (1.1) has been confirmed experimentally [22]. Note that the hydrodynamic mechanism is not directly implied by Eq.…”

Section: Introductionmentioning

confidence: 83%

“…According to Brochard [16], the forces acting on the droplet include the driving force due to the wettability gradient and the viscous drag force. To balance these two forces (with a negligible inertia effect), the droplet attains a steady state with an almost constant migration velocity V mig given by [16,21,22]…”

Section: Introductionmentioning

confidence: 99%

“…The magnitude of α V depends on the hydrodynamic mechanism that resolves the stress singularity at the three-phase contact line [5,16,22]. Theoretically, α V is a constant provided that the drag forces in the vicinity of the contact line scale with the fluid viscosity in the bulk region [22].…”

Section: Introductionmentioning

confidence: 99%

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Droplet motion in one-component fluids on solid substrates with wettability gradients

Qian

2012

Phys. Rev. E

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CitationDroplet motion in one-component fluids on solid substrates with wettability gradients 2012, 85 (5) Physical Review E Droplet motion on solid substrates has been widely studied not only because of its importance in fundamental research but also because of its promising potentials in droplet-based devices developed for various applications in chemistry, biology, and industry. In this paper, we investigate the motion of an evaporating droplet in onecomponent fluids on a solid substrate with a wettability gradient. As is well known, there are two major difficulties in the continuum description of fluid flows and heat fluxes near the contact line of droplets on solid substrates, namely, the hydrodynamic (stress) singularity and thermal singularity. To model the droplet motion, we use the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] for the hydrodynamic equations in the bulk region, supplemented with the boundary conditions at the fluid-solid interface. In this continuum hydrodynamic model, various physical processes involved in the droplet motion can be taken into account simultaneously, e.g., phase transitions (evaporation or condensation), capillary flows, fluid velocity slip, and substrate cooling or heating. Due to the use of the phase field method (diffuse interface method), the hydrodynamic and thermal singularities are resolved automatically. Furthermore, in the dynamic van der Waals theory, the evaporation or condensation rate at the liquid-gas interface is an outcome of the calculation rather than a prerequisite as in most of the other models proposed for evaporating droplets. Numerical results show that the droplet migrates in the direction of increasing wettability on the solid substrates. The migration velocity of the droplet is found to be proportional to the wettability gradients as predicted by Brochard [Langmuir 5, 432 (1989)]. The proportionality coefficient is found to be linearly dependent on the ratio of slip length to initial droplet radius. These results indicate that the steady migration of the droplets results from the balance between the (conservative) driving force due to the wettability gradient and the (dissipative) viscous drag force. In addition, we study the motion of droplets on cooled or heated solid substrates with wettability gradients. The fast temperature variations from the solid to the fluid can be accurately described in the present approach. It is observed that accompanying the droplet migration, the contact lines move through phase transition and boundary velocity slip with their relative contributions mostly determined by the slip length. The results presented in this paper may lead to a more complete understanding of the droplet motion driven by wettability gradients with a detailed picture of the fluid flows and phase transitions in the vicinity of the moving contact line.

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Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

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Droplet motion in one-component fluids on solid substrates with wettability gradients

Qian

2012

Phys. Rev. E

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“…It is well known that interfacial properties of a solid substrate on the macroscale, such as wetting and adhesion, are determined by features of the surface on smaller scales. A number of examples of small-scale influence have been reported, both reversible (11-13) and nonreversible (14)(15)(16)(17)(18). Each of these modifies the surface by a mechanism different from the exposure and shielding of droplets.…”

Section: [3]mentioning

confidence: 99%

The electroosmotic droplet switch: Countering capillarity with electrokinetics

Vogel

Ehrhard

Steen

2005

Proc. Natl. Acad. Sci. U.S.A.

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Electroosmosis, originating in the double-layer of a small liquidfilled pore (size R) and driven by a voltage V, is shown to be effective in pumping against the capillary pressure of a larger liquid droplet (size B) provided the dimensionless parameter R 2 ͞ ͦ ͦVB is small enough. Here is surface tension of the droplet liquid͞gas interface, is the liquid dielectric constant, and is the zeta potential of the solid͞liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as V ϳ R 2 ͞B. Accordingly, the voltage needed to pump against smaller higherpressure droplets can actually decrease provided the pump poresize scales down with droplet size appropriately. The technological implication of this favorable scaling is that electromechanical transducers made of moving droplets, so-called ''droplet transducers,'' become feasible. To illustrate, we demonstrate a switch whose bistable energy landscape derives from the surface energy of a droplet-droplet system and whose triggering derives from the electroosmosis effect. The switch is an electromechanical transducer characterized by individual addressability, fast switching time with low voltage, and no moving solid parts. We report experimental results for millimeter-scale droplets to verify key predictions of a mathematical model of the switch. With millimeter-size water droplets and micrometer-size pores, 5 V can yield switching times of 1 s. Switching time scales as B 3 ͞VR 2 . Two possible ''grab-and-release'' applications of arrays of switches are described. One mimics the controlled adhesion of an insect, the palm beetle; the other uses wettability to move a particle along a trajectory.bistability ͉ controlled adhesion ͉ electroosmotic pump ͉ palm beetle ͉ electro-capillary transducer T he natural tendencies of surface tension alone can move liquid between two small droplets. Droplets initially of different curvatures and connected by a liquid-filled conduit come to rest in one of two stable configurations owing to capillarity (recognized for connected bubbles, by ref. 1). The pumping action of electroosmosis can move liquid against this capillary force. A voltage signal applied to an electroosmotic pump positioned between the two droplets precisely controls toggling between the two configurations. This action characterizes the ''electroosmotic droplet switch'' (EODS), whose behavior and potential applications are the subject of this work.This work begins with a description of the system, including a discussion of the bistable nature of the two-droplet system and the model of flow in the EODS. Next, we provide validating data for the model based on time-dependent operation of the device. Model predictions include the parameter limits for successful switching and the time needed to switch the system between stable states. Scaling laws, indicating favorable operation of the EODS down to micrometer-size droplets, are then discussed. Finally, two examples of applications are suggested through demonstrations of unit operations of the...

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“…Since their studies were reported, not only the droplet motions due to surface-chemical gradients but also those due to morphological gradients have been extensively studied, [6][7][8][9][10][11][12][13] and many different methods generating wettability gradients have been developed. [14][15][16][17] The droplet motions induced by wettability gradients have a merit that they do not require any power source, while they have a demerit that the production of wettability gradient surface is often sophisticated and/or costly: the production usually requires such specialized techniques as self-assembled monolayer, polymer, lithography, and electrochemical etching.…”

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confidence: 99%

Spontaneous Motion of a Nitrobenzene Droplet on Au Electrode during Sn Electrodeposition

Mukouyama

Shiono

2015

J. Electrochem. Soc.

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The spontaneous motion of a nitrobenzene droplet on an Au electrode during an Sn electrodeposition has been reported in a previous paper (Chemphyschem, 9, 2302(Chemphyschem, 9, (2008). It also mentions that the velocity of the motion increases with a negative shift in the electrode potential. This present work has studied the motive force inducing the droplet motion, which is the imbalance between interfacial tension acting on the opposite side of a nitrobenzene droplet. As explained in the previous study, a high interfacial tension on the front side of the droplet is caused by an occurrence of electrodeposition. From this study, a low interfacial tension on the rear side has been found to attribute to an occurrence of hydrogen evolution reaction on the electrode surface. The rate of hydrogen evolution reaction increases as the electrode potential decreases, and thus the increase in the droplet velocity with a decreasing potential can be ascribed to the increase in the rate of hydrogen evolution reaction. The present work also reports that the velocity also increases by the addition of a salt such as K 2 SO 4 to the solutions. Wetting properties of solid surfaces are of interest from the viewpoint of interaction between liquid and solid phases. They play important roles not only in industrial processes but also in human activities. The wettability of a solid surface can be characterized by the contact angle of a liquid droplet on the solid surface.1,2 Figure 1 illustrates cross sections of oil droplets placed on solid surfaces in water (aqueous) phases. The contact angle of the droplet (θ) is defined by the mechanical equilibrium at the interface under the action of three interfacial tension (see Figure 1a), i.e., interfacial tension of solidwater interface (γ SW ), that of the solid-oil interface (γ SO ), and that of the oil-water interface (γ OW ), as expressed in the following Young's equation.1,2Comprehensive studies have demonstrated that a liquid droplet on a solid surface moves spontaneously due to an imbalance of interfacial tension acting on the droplet, as summarized in literatures. 2,3 As for an oil droplet on a solid surface in a water phase, the difference of γ SW between the front and rear sides of the droplet generates a driving force for the droplet to move spontaneously in the direction of a high interfacial tension, i.e., toward the region of higher wettability, as illustrated in Figure 1b.In the early 1990s, Ondarçuhu and Veyssie studied the behavior of a liquid droplet that was deposited on a boundary line between hydrophilic and hydrophobic parts of a plate. 4 The droplet moved spontaneously toward the region of higher wettability, and then stopped when the rear side of the droplet reached the boundary line. Chaudhury and Whitesides reported a spontaneous droplet motion induced by a wettability gradient on a solid surface.5 They generated a surfacechemical gradient on a silicon wafer surface by exposing it to the diffusing front of a vapor of decyltrichlorosilane.Since their studies were r...

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Ratcheting Motion of Liquid Drops on Gradient Surfaces

Cited by 202 publications

References 31 publications

Droplet motion in one-component fluids on solid substrates with wettability gradients

Droplet motion in one-component fluids on solid substrates with wettability gradients

The electroosmotic droplet switch: Countering capillarity with electrokinetics

Spontaneous Motion of a Nitrobenzene Droplet on Au Electrode during Sn Electrodeposition

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