Activated drops: Self-excited oscillation, critical speeding and noisy transport

Noise-Activated Fast Locomotion of DNA through the Frictional Landscape of Nanoporous Gels

It is hypothesized that nonlinear solid friction between the gel matrix and DNA molecules inhibits the motion of DNA through the nanopores of the gel during electrophoresis. In this article, it is demonstrated that external noise can alleviate the effect of solid friction, thus enhancing the mobility of DNA in an electrophoretic setting. In the presence of noise, the mobility of DNA increases by more than ∼113% compared to conventional electrophoresis. Although at a high power of noise, DNA exhibits Arrhenius kinetics, at a low power of noise, super-Arrhenius kinetics suggests the collective behavior of the activated motion of DNA molecules. A stochastic simulation following modified Langevin dynamics with the asymmetric pore size distribution of the agarose gel successfully predicts the mobility of DNA molecules and reveals the salient features of the overall dynamics. This "noise lubricity" may have a broader applicability from molecular to macroscopic locomotion.

Dynamic contact line lithography: Template-less complex Meso-patterning with polystyrene and poly(methyl methacrylate)

HYPOTHESIS

Micro/nanopatterning on a 2D surface is apt for cutting-edge miniaturization technology, which directly or indirectly requires high-end expensive lithographic tools. The evaporative deposition at the receding contact-line of a polymer solution, termed as Dynamic Contact Line Lithography (DCLL), can be a potential inexpensive technique for template-less meso-patterning if the deposition patterns from DCLL can be predicted a priori.

EXPERIMENTS

A deposition map (morphological phase diagram) from the myriads of patterns is constructed in terms of contact-line velocity and the polymer concentration. Specifically, two combinations: polystyrene (PS)/cyclohexane and poly (methyl methacrylate) (PMMA)/toluene are used to show the generic nature of the phase diagrams. The surface wettability of Si (water contact angle, CA ~15°) is tuned from CA ~35° to ~98° by patterning with DCLL.

FINDINGS

Directed by the phase diagrams, fabrication of a complex rectangular cross-pattern of PS and PMMA micro-threads with a periodicity of ~65 μm and ~50 μm respectively on a Si surface is demonstrated to establish the robustness and potential of the DCLL and predictive phase diagram.

Toward Controlling Evaporative Deposition: Effects of Substrate, Solvent, and Solute

Understanding evaporative deposition from a colloidal suspension and on-demand control over it are important due to its industrial and biomedical applications. In particular, it is known that interactions among substrate, solute, and solvent have important consequences on evaporative depositions; however, how these are affecting the deposition patterns and at which conditions these interactions are prominent need detailed investigations. Here we report that the total time of deposition (t_d) and the geometric shape of the droplet (L_c = initial footprint diameter/height) have a significant role in determining the evaporative deposition patterns. We have identified four zones based on t_d and L_c, and found that with longer deposition time (high t_d) and larger available space for particle motion within a liquid droplet (high L_c), deposition patterns were governed by the interactions among the substrate, solute, and solvent. We also experimentally demonstrated that the pinned contact line is indispensable for the "coffee ring" effect by comparing the deposition on surfaces with and without hysteresis. The effect of the Marangoni flow is also discussed, and it is shown that by controlling Marangoni flow, one can manipulate the droplet deposition from uniform disk-like to coffee ring with a central deposition.

Electrodynamic-contact-line-lithography with nematic liquid crystals for template-less E-writing of mesopatterns on soft surfaces

We report the development of a single-step, template-less and fast pathway, namely, Electrodynamic-Contact-Line-Lithography (ECLL), to write micro to nanopatterns on the surface of a soft polymer film. As a model system, a layer of nematic liquid crystals (NLC), resting on a polymer thin film, was sandwiched between a pair of electrodes emulating the electrowetting on a dielectric (EWOD) setup. Upon the application of electric field, the Maxwell stresses thus generated at the NLC-polymer interface due to the high dielectric contrast stimulated an unprecedented fingering instability at the advancing NLC-polymer-air contact line. In the process, the advancing electrospreading front of NLC left the footprint of an array of micro to nanoscale wells on the polymer surface with a long-range ordering thus unveiling a pathway for maskless patterning of a soft elastic film. Unlike the conventional electric field induced lithography (EFL), the meso-scale morphology was found to follow the short wavelength-scales as the periodicity of the patterns (λ_c) varied linearly with the thickness of the film (h), (λ_c∝h). The high dielectric contrast at the NLC-polymer interface and the local fluctuation of the NLC directors ensured a time scale much faster than the same observed for the polymer-air systems.

Designing biomimetic liquid diodes

Just as the innovation of electronic diodes that allow the current to flow in one direction provides a foundation for the development of digital technologies, the engineering of surfaces or devices that allow the directional and spontaneous transport of fluids, termed liquid diodes, is highly desired in a wide spectrum of applications ranging from medical microfluidics, advanced printing, heat management and water collection to oil-water separation. Recent advances in manufacturing, visualization techniques, and biomimetics have led to exciting progress in the design of various liquid diodes. In spite of exciting progress, formulating a general framework broad enough to guide the design, optimization and fabrication of engineered liquid diodes remains a challenging task to date. In this review, we first present an overview of the development of biological and engineered liquid diodes to elucidate how to control the surface chemistry and topography to regulate the transport of liquids without the need for external energy. Then the latest design strategies allowing for the creation of longitudinal and transverse liquid diodes are discussed and compared. We also define some figures of merit such as the rectification coefficient and the transport velocity and distance to quantify the performance of liquid diodes. Finally, we highlight perspectives on the development of engineered liquid diodes that transcend nature and adapt to various practical applications.

Simultaneous Multidrop Creation with Superhydrophobic Wells for Field Environmental Sensing of Nanoparticles

Facile creation of multiple drops at appropriate volumes on surfaces without the use of sophisticated instrumentation facilitates downstream evaporative preconcentration of liquid samples for analytical purposes. In this work, a superhydrophobic (SH) substrate comprising wells with a perforated mesh base was developed for simultaneous drop creation in a quick and convenient manner. In contrast to the method of pouring liquid directly over the SH wells, consistent liquid filling was readily achieved by a simple immersion approach. This method works well even for challenging situations where well diameters are smaller than 3.4 mm. Despite the poor liquid-retention properties of SH surfaces, inverting the wells did not result in liquid detachment under gravitational force, indicating strong pinning effects afforded by the well architecture. The perforated base of the well allowed the liquid to be completely removed from the well by compressed air. High-speed camera image processing was used to study the evolution of drop contact angle and displacement with time. It was found that the liquid body was able to undergo strong oscillations. Optical spectroscopy was used to confirm the ability of evaporative preconcentration of silver nanoparticles.

Mapping microscale wetting variations on biological and synthetic water-repellent surfaces

Droplets slip and bounce on superhydrophobic surfaces, enabling remarkable functions in biology and technology. These surfaces often contain microscopic irregularities in surface texture and chemical composition, which may affect or even govern macroscopic wetting phenomena. However, effective ways to quantify and map microscopic variations of wettability are still missing, because existing contact angle and force-based methods lack sensitivity and spatial resolution. Here, we introduce wetting maps that visualize local variations in wetting through droplet adhesion forces, which correlate with wettability. We develop scanning droplet adhesion microscopy, a technique to obtain wetting maps with spatial resolution down to 10 µm and three orders of magnitude better force sensitivity than current tensiometers. The microscope allows characterization of challenging non-flat surfaces, like the butterfly wing, previously difficult to characterize by contact angle method due to obscured view. Furthermore, the technique reveals wetting heterogeneity of micropillared model surfaces previously assumed to be uniform.

Topological liquid diode

The last two decades have witnessed an explosion of interest in the field of droplet-based microfluidics for their multifarious applications. Despite rapid innovations in strategies to generate small-scale liquid transport on these devices, the speed of motion is usually slow, the transport distance is limited, and the flow direction is not well controlled because of unwanted pinning of contact lines by defects on the surface. We report a new method of microscopic liquid transport based on a unique topological structure. This method breaks the contact line pinning through efficient conversion of excess surface energy to kinetic energy at the advancing edge of the droplet while simultaneously arresting the reverse motion of the droplet via strong pinning. This results in a novel topological fluid diode that allows for a rapid, directional, and long-distance transport of virtually any kind of liquid without the need for an external energy input.

Energy Dissipation of Moving Drops on Superhydrophobic and Superoleophobic Surfaces

A water drop moving on a superhydrophobic surface or an oil drop moving on a superoleophobic surface dissipates energy by pinning/depinning at nano- and microprotrusions. Here, we calculate the work required to form, extend, and rupture capillary bridges between the protrusions and the drop. The energy dissipated at one protrusion W_S is derived from the observable apparent receding contact angle Θ_r^app and the density of protrusions n by W_s = γ(cos Θ_r^app + 1)/n, where γ is the surface tension of the liquid. To derive an expression for W_s that links the microscopic structure of the surface to apparent contact angles, two models are considered: A superhydrophobic array of cylindrical micropillars and a superoleophobic array of stacks of microspheres. For a radius of a protrusion R and a receding materials contact angle Θ_r, we calculate the energy dissipated per protrusion as W_s = πγR²[A - ln(R/κ)]f(Θ_r). Here, A = 0.60 for cylindrical micropillars and 2.9 for stacks of spheres. κ is the capillary length. f(Θ_r) is a function which depends on Θ_r and the specific geometry, f ranges from ≈0.25 to 0.96. Combining both equations above, we can correlate the macroscopically observed apparent receding contact angle with the microscopic structure of the surface and its material properties.

Remodeling of Super-hydrophobic Surfaces

An experimental study on the underlying mechanisms of structured super-hydrophobic surfaces was recently published [ Butt, H.-J.; et al. How Water Advances on Superhydrophobic Surfaces. Phys. Rev. Lett. 2016, 116, 096101 . DOI: 10.1103/PhysRevLett.116.096101 ]. After depositing small drops of water, Butt's group inclined their surfaces to initiate movement. They examined the contact between the water and structured surfaces with confocal microscopy. They observed that drops were suspended atop the protruding features and movement of water was different at the advancing and receding edges. At the advancing edge, the water interface descended downward and draped itself across the features. At the receding edge, water jumped from one feature to the next. As Butt and co-workers did not test their data against any existing model, that is done in this paper. Here, a previously proposed model that employs linear averaging at the contact line was adapted to their surfaces in an attempt to estimate their contact and sliding angles. Predictions from the model generally agreed with their experimental measurements.

Linear Stepper Actuation Driving Drop Resonance and Modifying Hysteresis

In this work, 2 μL water drops are placed on substrates that are created to have a circular hydrophilic region bounded by superhydrophobicity so that they exhibit high contact angles. When the substrate is translated by a linear stepper actuator, the random force components present in the actuator are shown to cause the drop to rock resonantly. When the substrate is translated downward at inclination angles of up to 6° with respect to the horizontal, the contact angle hysteresis increases progressively to a limiting condition. When the substrate is moved up at inclined angles, alternatively, the contact angle hysteresis increases initially to the limiting condition before it is progressively restored to its static state. These behaviors are accounted for by the reversible micro-Cassie to Wenzel wetting state transformations that are made possible by the hierarchical microscale and nanoscale structures present in the superhydrophobic regions.

Liquid-body resonance while contacting a rotating superhydrophobic surface

We advance a scheme in which a liquid body on a stationary tip in contact with a rotating superhydrophobic surface is able to maintain resonance primarily from stick-slip events. With tip-to-surface spacing in the range 2.73 ≤ h < 2.45 mm for a volume of 10 μL, the liquid body was found to exhibit resonance independent of the speed of the drum. The mechanics were found to be due to a surface-tension-controlled vibration mode based on the natural frequency values determined. With spacing in the range 2.45 ≤ h < 2.15 mm imposed for a volume of 10 μL, the contact length of the liquid body was found to vary with rotation of the SH drum. This was due to the stick-slip events being able to generate higher energy fluctuations causing the liquid-solid contact areas to vary since the almost oblate spheroid shape of the liquid body had intrinsically higher surface energies. This resulted in the natural frequency perturbations being frequency- and amplitude-modulated over a lower frequency carrier. These findings have positive implications for microfluidic sensing.

Generation of Motion of Drops with Interfacial Contact

A liquid drop moves on a solid surface if it is subjected to a gradient of wettability or temperature. However, the pinning defects on the surface manifested in terms of a wetting hysteresis, or first-order nonlinear friction, limit the motion in the sense that a critical size has to be exceeded for a drop to move. The effect of hysteresis can, however, be mitigated by an external vibration that can be either structured or stochastic, thereby creating a directed motion of the drop. Many of the well-known features of rectification, amplification, and switching that are generic to electronics can be engineered with such types of movements. A specific case of interest is the random coalescence of drops on a surface that gives rise to self-generated noise. This noise overcomes the pinning potential, thereby generating a random motion of the coalesced drops. Randomly moving coalesced drops themselves exhibit a directed diffusive flux when a boundary is present to eliminate them by absorption. With the presence of a bias, the coalesced drops execute a diffusive drift motion that can have useful applications in various water and thermal management technologies.

Diminution of contact angle hysteresis under the influence of an oscillating force

We suggest a simple quantitative model for the diminution of contact angle hysteresis under the influence of an oscillatory force invoked by thermal fluctuations, substrate vibrations, acoustic waves, or oscillating electric fields. Employing force balance rather than the usual description of contact angle hysteresis in terms of Gibbs energy, we highlight that a wetting system, such as a sessile drop or a bubble adhered to a solid substrate, appears at long times to be partially or fully independent of contact angle hysteresis and thus independent of static friction forces, as a result of contact line pinning. We verify this theory by studying several well-known experimental observations such as the approach of an arbitrary contact angle toward the Young contact angle and the apparent decrease (or increase) in an advancing (or a receding) contact angle under the influence of an external oscillating force.

Free-decay and resonant methods for investigating the fundamental limit of superhydrophobicity

The recently demonstrated extremely water-repellent surfaces with contact angles close to 180° with nearly zero hysteresis approach the fundamental limit of non-wetting. The measurement of the small but non-zero energy dissipation of a droplet moving on such a surface is not feasible with the contemporary methods, although it would be needed for optimized technological applications related to dirt repellency, microfluidics and functional surfaces. Here we show that magnetically controlled freely decaying and resonant oscillations of water droplets doped with superparamagnetic nanoparticles allow quantification of the energy dissipation as a function of normal force. Two dissipative forces are identified at a precision of ~ 10 nN, one related to contact angle hysteresis near the three-phase contact line and the other to viscous dissipation near the droplet-solid interface. The method is adaptable to common optical goniometers and facilitates systematic and quantitative investigations of dynamical superhydrophobicity, defects and inhomogeneities on extremely superhydrophobic surfaces.

Water drop friction on superhydrophobic surfaces

To investigate water drop friction on superhydrophobic surfaces, the motion of water drops on three different superhydrophobic surfaces has been studied by allowing drops to slide down an incline and capturing their motion using high-speed video. Two surfaces were prepared using crystallization of an alkyl ketene dimer (AKD) wax, and the third surface was the leaf of a Lotus (Nelumbo Nucifera). The acceleration of the water droplets on these superhydrophobic surfaces was measured as a function of droplet size and inclination of the surface. For small capillary numbers, we propose that the energy dissipation is dominated by intermittent pinning-depinning transitions at microscopic pinning sites along the trailing contact line of the drop, while at capillary numbers exceeding a critical value, energy dissipation is dominated by circulatory flow in the vicinity of the contacting disc between the droplet and the surface. By combining the results of the droplet acceleration with a theoretical model based on energy dissipation, we have introduced a material-specific coefficient called the superhydrophobic sliding resistance, b(sh). Once determined, this parameter is sufficient for predicting the motion of water drops on superhydrophobic surfaces of a general macroscopic topography. This theory also infers the existence of an equilibrium sliding angle, β(eq), at which the drop acceleration is zero. This angle is decreasing with the radius of the drop and is in quantitative agreement with the measured tilt angles required for a stationary drop to start sliding down an incline.