Gradient Induced Droplet Motion Over Soft Solids

Journal of Colloid and Interface Science, 2008

Directional movement of liquid droplets is of significance not only for certain physiological processes in nature but also for design of some microfluidic devices. In this study, we report a novel way to drive directional movement of liquid droplets on a microbeam with a varying or gradient stiffness. We use the energy method to theoretically analyze the interaction between a droplet and the elastic microbeam. The system tends to have the minimum potential energy when the droplet moves to the softer end of the beam. Therefore, a gradient change of the bending stiffness may be utilized to help the directional motion of droplets. Similarly, one can also drive droplets to move in a designed direction by varying the cross sectional geometry of the beam. Finally, some possible applications of this self-propelling mechanism are suggested.

Physical Review E, 2012

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.

EPL (Europhysics Letters), 2012

We study the depinning and subsequent motion of two-dimensional droplets with large contact angles that are driven by a body force on flat substrates decorated with a sinusoidal wettability pattern. To this end, we solve the Stokes equation employing a boundary element method. At the substrate a Navier slip condition and a spatially varying microscopic contact angle are imposed. Depending on the substrate properties, we observe a range of driving forces where resting and periodically moving droplets are found, even though inertial effects are neglected. This is possible in the considered overdamped regime because additional energy is stored in the non-equilibrium configuration of the droplet interfaces. Finally, we present the dependence of the driving at de-and repinning on wettability contrast and slip length, complemented by a bifurcation analysis of pinned-droplet configurations.

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2018

Despite the extensive study of wetting in literature, there are still many unresolved issues regarding forced wetting. One of them refers to the effect of the initial droplet shape on the force required for spreading and sliding along a solid surface; an effect that has not ever been explicitly reported. Previous experimental works, in general, assume initially axisymmetric droplet shapes. In this study, experiments are performed with an innovative device, Kerberos, capable of subjecting sessile droplets at different tilting angles to varying centrifugal forces in order to explore the spreading/sliding behavior of droplets of different volumes and different initial shapes (including non-axisymmetric). A broad validation of the technique is achieved by the repeatability and consistency of measurements. Results for initially axisymmetric and non-axisymmetric droplets concerning contact angles, droplet length, droplet shape and velocity are presented and discussed. Furthermore, detailed results for the critical tangential accelerations required for the inception of spreading and sliding are presented showing the different sensitivity of these parameters on the droplet initial shape. Experimental results are employed to test the applicability of the well-known Furmidge equation for the retention force in the case of initially non-axisymmetric droplets. On this account, the initial length of droplets is found to be a more appropriate length scale in the Furmidge equation than the initial droplet width.

The aim of this study is to formulate and solve the equiiibrium shape of a liquid droplet of contact radius r. in the middle of anelastic isotropic thin solid sheet of radius I, by using the different surface concepts such as surface free energy and surface stress. This is achieved by determining the form of the interfaces as a result of minimization of the total free energy of the system. The profiles are obtained from integration of Euler’s differential equations. An interpretation of these equations is given in terms of mechanical forces. In the domain 0 < r < ro, normal to the sheet there act two shearing forces. One of them derives from Laplace’s overpressure inside the drop. It is uniformly distributed over the area rrg. The other one, coming from the total surface stress of the sheet, leads to shearing forces proportional to the local slope. Outside the drop (rc < r < I), there are at the same two types of normal shearing forces, one due to tbe surface stress, the other type acting on the triple line of length 2rrr,. Each of these mechanical forces acts on distinct domains of the sheet. Therefore it is not allowed to superpose these forces acting on the entire sheet 0 < r < 1. If such a superposition is unduly made, a ridge appears at the triple line. The liquid drop is found to be spherical as expected in the absence of gravity. If gravity acts, qualitative modifications are discussed. The profile of the sheet is pseudo-parabolic with an inflection circle of radius ri changing within 0 < ri < 1 according to the fastening ratio l/r, of the sheet. The sag under the drop depends on the Lapiace overpressure and the flexure rigidity D of the sheet. Our general result is easily brought to the special cases where the droplet lies either on a membrane or on another liquid surface.

2014

The behavior of a liquid droplet settled on an energetically heterogeneous surface has been studied by a simulation method. The surface energetic inhomogeneities were represented by a pattern of alternating and parallel strips of two different contact angles and of gradually changing width, but of the average wettability of the surface remaining constant. It was observed that the isotropic random forces acting on the droplet induced its highly asymmetric movement. The observed droplet shift occurred along the gradient of the size of heterogeneities and was directed to increasing width of the strips. The influence of some model parameters on the trajectory of the droplet has been discussed.

2013

Making small liquid droplets move spontaneously on solid surfaces is a key challenge in lab-on-chip and heat exchanger technologies. Here, we report that a substrate curvature gradient can accelerate micro-and nanodroplets to high speeds on both hydrophilic and hydrophobic substrates. Experiments for microscale water droplets on tapered surfaces show a maximum speed of 0.42 m=s, 2 orders of magnitude higher than with a wettability gradient. We show that the total free energy and driving force exerted on a droplet are determined by the substrate curvature and substrate curvature gradient, respectively. Using molecular dynamics simulations, we predict nanoscale droplets moving spontaneously at over 100 m=s on tapered surfaces.

Computational fluid dynamics (cfd) is used to study the effect of contact angle on droplet shape as it moves through a contraction. A new non-dimensional number is proposed in order to predict situations where the deformed droplet will form a slug in the contraction and thus interact with the channel wall. We argue that droplet flow into a contraction is a useful method to ensure that a droplet will wet a channel surface without a trapped lubrication film. We demonstrate that when a droplet is larger than a contraction, capillary and

Langmuir, 2004

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.