Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Motion of liquid drops on surfaces induced by asymmetric vibration: role of contact angle hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.     

A unique behavior of water drops induced by low-density polyethylene surface with a sharp wettability transition

A low-density polyethylene (LDPE) surface with a sharp wettability gradient and high hysteresis was prepared, on which a unique behavior of water drops was found. The water contact angle of one water drop on the less hydrophobic region was larger than that on the more hydrophobic end, which was much different from the general phenomenon. The unique behavior is believed to be induced by the high hysteresis of the LDPE surface and the sharp change in wettability. The driving and hysteresis forces acting on the water drops were calculated and analyzed in detail. The reasons resulting to such a unique phenomenon were further explained.     

Experiments on the motion of drops on a horizontal solid surface due to a wettability gradient

Results from experiments performed on the motion of drops of tetraethylene glycol in a wettability gradient present on a silicon surface are reported and compared with predictions from a recently developed theoretical model. The gradient in wettability was formed by exposing strips cut from a silicon wafer to dodecyltrichlorosilane vapors. Video images of the drops captured during the experiments were subsequently analyzed for drop size and velocity as functions of position along the gradient. In separate experiments on the same strips, the static contact angle formed by small drops was measured and used to obtain the local wettability gradient to which a drop is subjected. The velocity of the drops was found to be a strong function of position along the gradient. A quasi-steady theoretical model that balances the local hydrodynamic resistance with the local driving force generally describes the observations; possible reasons for the remaining discrepancies are discussed. It is shown that a model in which the driving force is reduced to accommodate the hysteresis effect inferred from the data is able to remove most of the discrepancy between the observed and predicted velocities.     

The movement of a water droplet on a gradient surface prepared by photodegradation

A hydrophobic to hydrophilic gradient surface was prepared using the tuned photodegradation of an alkylsilane self-assembled monolayer (SAM) using irradiation of vacuum ultraviolet light (wavelength=172 nm). The water contact angle on the photodegraded SAM surface was adjusted using the intensity and time photoirradiation parameters. The formation of a gradient was confirmed by fluorescent labeling. The water drop moved from the hydrophobic to hydrophilic surface with a velocity that depended on the gradient. The higher the gradient, the faster the water moved. For the first time, we have prepared a gradient surface using photodegradation where the movement of a water drop was regulated by the degree of gradation. Considering that the photodegradation technique can be applied to various surfaces and to lithography, this technique will be useful for various material surfaces.     

Vibration-actuated drop motion on surfaces for batch microfluidic processes

When a liquid drop is subjected to an asymmetric lateral vibration on a nonwettable surface, a net inertial force acting on the drop causes it to move. The direction and velocity of the drop motion are related to the shape, frequency, and amplitude of vibration, as well as the natural harmonics of the drop oscillation. Aqueous drops can be propelled through fluidic networks connecting various unit operations in order to carry out batch processing at the miniature scale. We illustrate the integration of several unit operations on a chip: drop transport, mixing, and thermal cycling, which are precursor steps to carrying out advanced biological processes at microscale, including cell sorting, polymerase chain reaction, and DNA hybridization.     

Brownian motion of a drop with hysteresis dissipation

Small water drops placed on a low-energy substrate with a slight tilt were vibrated parallel to the support with bands of Gaussian white noise of different powers. The drops drifted downward on the inclined support accompanied with random forward and backward movements. For a hysteresis free surface, the drift velocity should only be the product of the component of the gravitational acceleration and the Langevin relaxation time, being independent of the power of noise. On the other hand, in the presence of hysteresis, as is the case here, the drift velocity depends strongly on the power of the noise. This result illustrates the role of hysteresis in the drifted motion of drops on a surface subjected to vibration, which has important bearings on various forms of work fluctuation relations.     

Shape-gradient composite surfaces: water droplets move uphill

The approach of water droplets self-running horizontally and uphill without any other forces was proposed by patterning the shape-gradient hydrophilic material (i.e., mica) to the hydrophobic matrix (i.e., wax or low-density polyethylene (LDPE)). The shape-gradient composite surface is the best one to drive water droplet self-running both at the high velocity and the maximal distance among four different geometrical mica/wax composite surfaces. The driving force for the water droplets self-running includes: (1) the great difference in wettability of surface materials, (2) the low contact angle hysteresis of surface materials, and (3) the space limitation of the shape-gradient transportation area. Furthermore, the average velocity and the maximal distance of the self-running were mainly determined by the gradient angle (alpha), the droplet volume, and the difference of the contact angle hysteresis. Theoretical analysis is in agreement with the experimental results.     

Contact angle hysteresis on regular pillar-like hydrophobic surfaces

A series of pillar-like patterned silicon wafers with different pillar sizes and spacing are fabricated by photolithography and further modified by a self-assembled fluorosilanated monolayer. The dynamic contact angles of water on these surfaces are carefully measured and found to be consistent with the theoretical predictions of the Cassie model and the Wenzel model. When a water drop is at the Wenzel state, its contact angle hysteresis increases along with an increase in the surface roughness. While the surface roughness is further raised beyond its transition roughness (from the Wenzel state to the Cassie state), the contact angle hysteresis (or receding contact angle) discontinuously drops (or jumps) to a lower (or higher) value. When a water drop is at the Cassie state, its contact angle hysteresis strongly depends on the solid fraction and has nothing to do with the surface roughness. Even for a superhydrophobic surface, the contact angle hysteresis may still exhibit a value as high as 41 degrees for the solid fraction of 0.563.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.     

On some relations between advancing, receding and Young's contact angles

Problems of experimental determination and theoretical verification of equilibrium contact angles are discussed basing on the literature data. A relationship between the advancing and receding contact angles versus the equilibrium contact angle is described and then verified using the literature contact angles determined on paraffin wax and polypropylene. Using the proposed relationship and experimentally determined equilibrium contact angles, obtained by plotting the advancing and receding contact angles versus the contact angle hysteresis or by applying vibration of the system liquid drop/solid surface, it is found that the same value of the surface free energy for paraffin wax is calculated from the contact angles of water and ethylene glycol. However, in the case of polypropylene some inconsistency appears between the equilibrium contact angles of the probe liquid used and the calculated surface free energy. More experimental data of the equilibrium contact angle are needed to verify further the relationship.     

Liquid Drops on an Inclined Plane: The Relation between Contact Angles, Drop Shape, and Retentive Force

Contact angle hysteresis, drop shape, and drop retention were studied with a tiltable plane. Contact liquids were water and ethylene glycol. Four polymers and silicon wafers were used as substrates. When the plane was inclined, the shape of drops distorted, exhibiting advancing and receding contact angles. Drops remained stationary until a critical angle of tilt was exceeded, and then they began to move. The difference in the advancing and receding contact angles, or contact angle hysteresis, ranged from 9° to 66°, depending on the liquid and the substrate. Roughness did not seem to influence the hysteresis as much as the chemical nature of the surfaces. Elongation and back-to-front asymmetry were greater on surfaces with high hysteresis. We found a linear correlation between the aspect ratio of drops and their contact angle hysteresis. Also, the retentive force increased with elongation of the drops.     

Thermophoresis in liquids: a molecular dynamics simulation study

Thermophoresis in liquids is studied by molecular dynamics simulation (MD). A theory is developed that divides the problem in the way consistent with the characteristic scales. MD is then conducted to obtain the solution of each problem, which is to be all combined for macroscopic predictions. It is shown that when the temperature gradient is applied to the nonconducting liquid bath that contains neutral particles, there occurs a pressure gradient tangential to the particle surface at the particle-liquid interface. This may induce the flow in the interfacial region and eventually the particle to move. This applies to the material system that interacts through van der Waals forces and may be a general source of the thermophoresis phenomenon in liquids. The particle velocity is linearly proportional to the temperature gradient. And, in a large part of the given temperature range, the particle motion is in the direction toward the cold end and decreases with respect to the temperature. It is also shown that the particle velocity decreases or even reverses its sign in the lowest limit of the temperature range or with a particle of relatively weak molecular interactions with the liquid. The characteristics of the phenomenon are analyzed in molecular details.     

Fluid transport in nanochannels induced by temperature gradients

We investigate the mechanisms of fluid transport driven by temperature gradients in nanochannels through molecular dynamics simulations. It is found that the fluid-wall interaction is critical in determining the flow direction. In channels of very low surface energy, where the fluid-wall binding energy ε(fw) is small, the fluid moves from high to low temperature and the flow is induced by a potential ratchet near the wall. In high surface energy channels, however, the fluid is pumped from low to high temperature and the pressure drop caused by the temperature gradient is the major driving force. In addition, as the fluid-wall interaction is strengthened, the flow flux assumes a maximum, where ε(fw) is close to the lower temperature T(L) of the channel and ε(fw)/kT(L) ≈ 1 is roughly satisfied.     

Condensation-induced wetting state and contact angle hysteresis on superhydrophobic lotus leaves

In this paper, we demonstrate how condensed moisture droplets wet classical superhydrophobic lotus leaf surfaces and analyze the mechanism that causes the increase of contact angle hysteresis. Superhydrophobic lotus leaves in nature show amazing self-cleaning property with high water contact angle (>150°) and low contact angle hysteresis (usually <10°), causing droplets to roll off at low inclination angles, in accordance with classical Cassie–Baxter wetting state. However, when superhydrophobic lotus leaves are wetted with condensation, the condensed water droplets are sticky and exhibit higher contact angle hysteresis (40–50°). Compared with a fully wetted sessile droplet (classical Wenzel state) on the lotus leaves, the condensed water droplet still has relatively large contact angle (>145°), suggesting that the wetting state deviates from a fully wetted Wenzel state. When the condensed water droplets are subjected to evaporation at room conditions, a thin water film is observed bridging over the micropillar structures of the lotus leaves. This causes the dew to stick to the surface. This result suggests that the condensed moisture does not uniformly wet the superhydrophobic lotus leaf surfaces. Instead, there occurs a mixed wetting state, between classical Cassie–Baxter and Wenzel states that causes a distinct increase of contact angle hysteresis. It is also observed that the mixed Cassie–Baxter/Wenzel state can be restored to the original Cassie–Baxter state by applying ultrasonic vibration which supplies energy to overcome the energy barrier for the wetting transition. In contrast, when the surface is fully wetted (classical Wenzel state), such restoration is not observed with ultrasonic vibration. The results reveal that although the superhydrophobic lotus leaves are susceptible to being wetted by condensing moisture, the configured wetting state is intermediate between the classical Cassie–Baxter and Wenzel states.     

类液体动态界面材料：近期应用进展

类液体表面是接枝了高度柔性分子刷从而表现出类液体特性的表面。典型的类液体表面一般通过在平坦固体表面上共价接枝具有极低玻璃化转变温度的聚合物分子刷（其玻璃化转变温度一般在零下100 ℃以下）制备而成。由于所接枝分子链具有类似流体的高度动态特性,能自由旋转与运动,各种极性或非极性液体在这类被称为“类液体”或“准液体”的表面上粘附力低,易滑落,表现出极低的接触角滞后。传统上,对这类表面的研究主要限于简单的疏水及疏油应用。最近几年,国内外课题组相继报道了关于类液体表面的一些非常独特的界面物理化学特性;对其功能和应用的研究,也从简单的疏水、疏油,拓展到微观无损输运、防垢、除冰、冷凝传热和高性能膜分离等领域。基于类液体表面功能化的类液体动态界面材料也因而成为一类具有广阔应用前景的新兴材料体系。本文将在介绍类液体表面概念的基础上,重点介绍类液体动态界面材料最新的功能和应用研究成果,并对其未来研究和应用空间进行展望。     

Contact angle hysteresis

In thermodynamic equilibrium, the contact angle is related by Young's equation to the interfacial energies. Unfortunately, it is practically impossible to measure the equilibrium contact angle. When for example placing a drop on a surface its contact angle can assume any value between the advancing Θ_a and receding Θ_r contact angles, depending on how the drop is placed. Θ_a − Θ_r is called contact angle hysteresis. Contact angle hysteresis is essential for our daily life because it provides friction to drops. Many applications, such as coating, painting, flotation, would not be possible without contact angle hysteresis. Contact angle hysteresis is caused by the nanoscopic structure of the surfaces. Here, we review our current understanding of contact angle hysteresis with a focus on water as the liquid. We describe appropriate methods to measure it, discuss the causes of contact angle hysteresis, and describe the preparation of surfaces with low contact angle hysteresis.     

Hydrodynamic interaction of a nonvolatile droplet with a planar surface of evaporating liquid

Hydrodynamic interaction between a nonvolatile droplet and an infinite planar surface of an evaporating or condensing liquid is studied theoretically with allowance for effects that are linear with respect to the Knudsen number. The motion of the droplet in the direction normal to the planar liquid surface is considered at low Reynolds numbers and gradients of a gaseous medium temperature and the concentration of the substance evaporating or condensing on the planar liquid surface given at an infinitely large distance from the droplet. The presence of a temperature gradient in the liquid is taken into account in the analysis. The problem is solved in a bispherical coordinate system. The velocity of the steady motion of a castor oil droplet is numerically estimated near the planar surface of evaporating water.     

A Modified Contact Angle Measurement Process to Suppress Oil Drop Spreading and Improve Precision

Static contact angle measurement is a widely applied method for wettability assessment. Despite its convenience, it suffers from errors induced by contact angle hysteresis, material heterogeneity, and other factors. This paper discusses the oil drop spreading phenomenon that was frequently observed during contact angle measurements. Experimental tests showed that this phenomenon is closely related to surfactants in the surrounding phase, the remaining oil on the rock surface, and oil inside the surrounding phase. A modified contact angle measurement process was proposed. In the modified method, deionized water was used as the surrounding phase, and a rock surface cleaning step was added. Subsequent measurements showed a very low chance of oil drop spreading and improved precision. A further comparison study showed that, when the surrounding phase was deionized water, the measured contact angle values tended to be closer to intermediate-wet conditions compared to the values measured in clean surfactant solutions. This difference became more significant when the surface was strongly water-wet or strongly oil-wet. As a result, the developed process has two prerequisites: that the in-situ contact angle values inside surfactant solutions are not required, and that the wettability alteration induced by the surfactant solution is irreversible.