Drastic changes in interfacial hydrodynamics due to wall slippage: slip-intensified film thinning, drop spreading, and capillary instability.

We report that wall slippage can drastically change both steady and dynamic flow characteristics for a wide class of free-surface thin film flows. This is demonstrated by (i) the breakdown of the 2/3 law and its replacement by a new quadratic law for the deposited film thickness in the Landau-Levich-Bretherton coating, (ii) the departure from de Gennes-Tanner's cubic law for dynamic contact angles in drop spreading, consequently resulting in much faster spreading than the classical Tanner law, and (iii) the exaggerated capillary instability of an annular film where a fractional amount of wall slip can lead to much more rapid draining and hence make the film more vulnerable to rupture. In (ii), the molecular precursor film is shown to have a length varying like the -1/2 power of the spreading speed, producing an anomalous 1/3 diffusion law governing its spreading dynamics. A variety of existing experimental findings can be well captured by the new scaling laws we derive. All these features are accompanied with no-slip-to-slip transitions, offering alternative means for probing slip boundaries.

Entropic trap, surface-mediated combing, and assembly of DNA molecules within submicrometer interfacial confinement.

In this work, we report an alternative microfluidic approach to studying the motion of single DNA molecules in an electric field. Making use of a closely fitting droplet in a microchannel, DNA molecules can be confined within the submicrometer film beneath the droplet. Several dynamic events at the single-molecule level and self-assembly phenomena at mesoscales are observed. We find that DNA can be trapped and stretched at the entrance to the film due to entropic effects. After escaping the trap, DNA can exhibit cyclic stick-slip motion with a field-dependent mobility owing to interim anchoring to surface surfactants. We also observe that, by incorporation of surface modification effects with plasma oxidation, DNA can be combed onto the channel surface at sufficiently high fields. In this case, upon removing the field, as-stretched DNA molecules can aggregate into larger clusters or self-organize into mesoscale bundles aligned in the direction of the previously applied field. The physics underlying these phenomena is discussed in detail.

Role of base flows on surfactant-driven interfacial instabilities.

In this paper, we examine how base flows affect interfacial stabilities in the presence of surfactants. A thin-film flow model, subjected to various base-flow conditions, is employed to mimic a wide class of practical interfacial flows. The base flow can be driven by an external force (e.g., pressure forcing or gravity), an interfacial stress, or their combination. For long-wave perturbations, we show that the stability is governed by a coupled set of evolution equations for the interface and surfactant concentration, so the origin of the stability can be unraveled analytically in line with simpler physical arguments. We also demonstrate that the system can exhibit a variety of stability states; it can be neutral, conditionally stable or unstable, or definitely stable or unstable, determined solely by the nature of the base flow and how it regulates surfactant transport. Two modes are found to determine the stability, the interface and surfactant modes, and characterized by the ratio of the basic interfacial shear force to the external force. The routes to the instability are also identified through the action of the base flow. The base flow plays a dual role in affecting the stability: although the imposition of an interfacial shear destabilizes the interface, an external force can cause stabilization. The competition between these two effects gives rise to stability or instability in a range of the force ratio. The underlying mechanisms are elucidated in detail. A generalized criterion for the onset of instability is also established for one- or two-fluid interfacial flows.

Conformational transitions of single polymer adsorption in poor solvent: Wetting transition due to molecular confinement induced line tension.

We report a theory capable of describing conformational transitions for single polymer adsorption in a poor solvent. We show that an additional molecular confinement effect near the contact line can act exactly like line tension, playing a critical role in the behavior of an absorbed polymer chain. Using this theory, distinct conformational states: desorbed globule (DG), surface attached cap (SAC), and adsorbed lens (AL), can be vividly revealed, resembling the drying-wetting transition of a nanodroplet. But the transitions between these states can behave rather differently from those in the usual wetting transitions. The DG-SAC transition is discrete, occurring at the adsorption threshold when the globule size at the desorbed state is equal to the adsorption blob. The SAC-AL transition is smooth for finite chain lengths, but can change to discontinuous in the infinite chain limit, characterized by the different end-to-end exponent 3/8 and the unique crossover exponent 1/4. Distinctive critical exponents near this transition are also determined, indicating that it is an additional universality class of phase transitions. This work also sheds light on nanodrop spreading, wherein the important role played by line tension might simply be a manifestation of the local molecular confinement near the contact line.

Superdiffusion in dispersions of active colloids driven by an external field and their sedimentation equilibrium.

The diffusive behaviors of active colloids with run-and-tumble movement are explored by dissipative particle dynamics simulations for self-propelled particles (force dipole) and external field-driven particles (point force). The self-diffusion of tracers (solvent) is investigated as well. The influences of the active force, run time, and concentration associated with active particles are studied. For the system of self-propelled particles, the normal diffusion is observed for both active particles and tracers. The diffusivity of the former is significantly greater than that of the latter. For the system of field-driven particles, the superdiffusion is seen for both active particles and tracers. In contrast, it is found that the anomalous diffusion exponent of the former is slightly less than that of the latter. The anomalous diffusion is caused by the many-body, long-range hydrodynamic interactions. In spite of the superdiffusion, the sedimentation equilibrium of field-driven particles can be acquired and the density profile is still exponentially decayed. The sedimentation length of field-driven particles is always greater than that of self-propelled particles.

Stability of a viscoelastic falling film with surfactant subjected to an interfacial shear.

The long-wavelength stability is analyzed for a surfactant-laden, viscoelastic liquid flowing down an inclined plane when the liquid undergoes additional interfacial shear. The upper convected Maxwell model is employed for describing the elastic nature of the fluid. The system stability is characterized by the interface and the surfactant modes. The interface mode involves both elastic and Marangoni effects that modulate the stability with applied shears and gravity-driven flow. The surfactant mode is only determined by the shear-induced Marangoni effects. A phase diagram is established to identify the dominant mode and the overall features of instability. It reveals that the system is susceptible to instability, except in a stable window when the applied shear opposes the gravity-driven flow.

Shear-modulated electroosmotic flow on a patterned charged surface.

The effect of imposing shear flow on a charge-modulated electroosmotic flow is theoretically investigated. The flow structures exhibit either saddle points or closed streamlines, depending on the relative strength of an imposed shear to the applied electric field. The formation of closed streamlines could be advantageous for trapping nondiffusive particles at desired locations. Different time periodic alternating flows and their corresponding particle trajectories are also examined to assess strategies for creating efficient mixing.

Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary.

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.

Focusing and trapping of DNA molecules by head-on ac electrokinetic streaming through join asymmetric polarization.

In this work, invoking join asymmetric ac polarization using double half-quadrupole electrodes in a symmetric arrangement, we demonstrate a head-on ac electro-osmotic streaming capable of focusing and trapping DNA molecules efficiently. This is manifested by the observation that picomolar DNA molecules can be trapped into a large crosslike spot with at least an order of magnitude concentration enhancement within just half a minute. We identify that the phenomenon is a combined result of the formation of two prefocused DNA jets flowing toward each other, dipole-induced attraction between focused DNA molecules, and dielectrophoretic trap on the spot. With an additional horizontal pumping, we observe that the trap can transform into a peculiar pitchfork streaming capable of continuous collection and long-distance transport of concentrated DNA molecules. We also show that the same electrode design can be used to direct assembly of submicrometer particles. This newly designed microfluidic platform not only has potentials in enhancing detection sensitivity and facilitating functional assembly for on-chip analysis but also provides an added advantage of transporting target molecules in a focused and continuous manner.

Dynamic double layer effects on ac-induced dipoles of dielectric nanocolloids.

Normal and tangential surface ionic currents around low-permittivity nanocolloids with surface charges are shown to produce three different conductive mechanisms for ac-induced dipoles, all involving dynamic space charge accumulation at the double layerbulk interface with a conductivity jump. However, the distinct capacitor dimensions and diffusive contributions produce three disparate crossover frequencies at which the induced dipole reverses direction relative to the bulk field. A highly conducting collapsed diffuse layer, with bulk ion mobility, renders the particle conductive and produces an ionic strength independent crossover frequency for weak electrolytes. A precipitous drop in crossover frequency occurs at high ionic strengths when charging occurs only at the poles through field focusing around the insulated colloid. A peculiar maximum in crossover frequency exists between these two asymptotes for colloids smaller than a critical size when normal charging of the diffuse layer occurs over the entire surface. The crossover frequency data for latex nanocolloids of various sizes in different electrolytes of wide ranging ionic strengths are collapsed by explicit theoretical predictions without empirical parameters.

Dynamic particle trapping, release, and sorting by microvortices on a substrate.

This paper examines particle trapping and release in confined microvortex flows, including those near a solid surface due to variations in the electrokinetic slip velocity and those at a liquid-gas interface due to an external momentum source. We derive a general analytical solution for a two-dimensional microvortex flow within a semicircular cap. We also use a bifurcation theory on the kinetic equation of particles under various velocity and force fields to delineate the conditions for a vortex trap, a point trap, a limit cycle trap, and the selective sorting of the particles into different traps. In the presence of only divergence-free forces on suspended particles, we find that two parameters, such as those related to Stokes drag, gravity, and flow vorticity, are sufficient to classify all the trap topologies for a given slip velocity distribution. We also show that nondivergence-free forces such as nonuniform repulsion or attraction can capture suspended particles in one trap and selectively sort a binary suspension into different traps.

Nonuniform electro-osmotic flow on charged strips and its use in particle trapping.

In this article, we investigate theoretically electro-osmotic flow set up by charged strips on an otherwise uncharged surface. Starting with a single-strip problem we demonstrate that for simple polynomial surface charge distributions several basic solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provide a more lucid way of revealing the flow features. These solutions reveal two types of flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and antisymmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions. We further extend the analysis to two uniformly charged strips and show how the flow characteristics vary with the strips' dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic vortices is also investigated theoretically for the first time. We show that in collaboration with short-range attraction effects the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.

Dynamic superconcentration at critical-point double-layer gates of conducting nanoporous granules due to asymmetric tangential fluxes.

A transient 10(6)-fold concentration of double-layer counterions by a high-intensity electric field is demonstrated at the exit pole of a millimeter-sized conducting nanoporous granule that permits ion permeation. The phenomenon is attributed to a unique counterion screening dynamics that transforms half of the surface field into a converging one toward the ejecting pole. The resulting surface conduction flux then funnels a large upstream electro-osmotic convective counterion flux into the injecting hemisphere toward the zero-dimensional gate of the ejecting hemisphere to produce the superconcentration. As the concentrated counterion is ejected into the electroneutral bulk electrolyte, it attracts co-ions and produce a corresponding concentration of the co-ions. This mechanism is also shown to trap and concentrate co-ion microcolloids of micron sizes too (macroions) and hence has potential application in bead-based molecular assays.

Long-range and superfast trapping of DNA molecules in an ac electrokinetic funnel.

In this work we report a microfluidic platform capable of trapping and concentrating a trace amount of DNA molecules efficiently. Our strategy invokes nonlinear electro-osmotic flow induced by charge polarization under high-frequency ac fields. With the asymmetric quadrupole electrode design, a unique converging flow structure can be created for generating focusing effects on DNA molecules. This focusing in turn transforms into a robust funnel that can collect DNA molecules distantly from the bulk and pack them into a compact cone with the aid of short-range dipole-induced self-attraction and dielectrophoresis. Our results reveal that not only can DNA molecules be concentrated within just a few seconds, but also they can be focused into threads of 1 mm in length, demonstrating the superfast and long-range trapping capability of this funnel. In addition, pico M DNA solutions can be concentrated with several decades of enhancement without any continuous feeding. Alternating concentration and release of DNA molecules is also illustrated, which has potentials in concentrating and transporting biomolecules in a continuous fashion using microdevices.

Electroosmotic flow in a microcavity with nonuniform surface charges.

In this work, we theoretically explore the characteristics of electroosmostic flow (EOF) in a microcavity with nonuniform surface charges. It is well known that a uniformly charged EOF does not give rise to flow separation because of its irrotational nature, as opposed to the classical problem of viscous flow past a cavity. However, if the cavity walls bear nonuniform surface charges, then the similitude between electric and flow fields breaks down, leading to the generation of vorticity in the cavity. Because this vorticity must necessarily diffuse into the exterior region that possesses a zero vorticity set by a uniform EOF, a new flow structure emerges. Assuming Stokes flow, we employ a boundary element method to explore how a nonuniform charge distribution along the cavity surface affects the flow structure. The results show that the stream can be susceptible to flow separation and exhibits a variety of flow structures, depending on the distributions of zeta potentials and the aspect ratio of the cavity. The interactions between patterned EOF vortices and Moffatt eddies are further demonstrated for deep cavities. This work not only has implications for electrokinetic flow induced by surface imperfections but also provides optimal strategies for achieving effective mixing in microgrooves.

A theoretical study on surfactant adsorption kinetics: effect of bubble shape on dynamic surface tension.

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.

Gravity-driven microfluidic particle sorting device with hydrodynamic separation amplification.

This paper describes a simple microfluidic sorting system that can perform size profiling and continuous mass-dependent separation of particles through combined use of gravity (1 g) and hydrodynamic flows capable of rapidly amplifying sedimentation-based separation between particles. Operation of the device relies on two microfluidic transport processes: (i) initial hydrodynamic focusing of particles in a microchannel oriented parallel to gravity and (ii) subsequent sample separation where positional difference between particles with different mass generated by sedimentation is further amplified by hydrodynamic flows whose streamlines gradually widen out due to the geometry of a widening microchannel oriented perpendicular to gravity. The microfluidic sorting device was fabricated in poly(dimethylsiloxane), and hydrodynamic flows in microchannels were driven by gravity without using external pumps. We conducted theoretical and experimental studies on fluid dynamic characteristics of laminar flows in widening microchannels and hydrodynamic amplification of particle separation. Direct trajectory monitoring, collection, and post-analysis of separated particles were performed using polystyrene microbeads with different sizes to demonstrate rapid (<1 min) and high-purity (>99.9%) separation. Finally, we demonstrated biomedical applications of our system by isolating small-sized (diameter <6 microm) perfluorocarbon liquid droplets from polydisperse droplet emulsions, which is crucial in preparing contrast agents for safe, reliable ultrasound medical imaging, tracers for magnetic resonance imaging, or transpulmonary droplets used in ultrasound-based occlusion therapy for cancer treatment. Our method enables straightforward, rapid, real-time size monitoring and continuous separation of particles in simple stand-alone microfabricated devices without the need for bulky and complex external power sources. We believe that this system will provide a useful tool to separate colloids and particles for various analytical and preparative applications and may hold potential for separation of cells or development of diagnostic tools requiring point-of-care sample preparation or testing.

Reversible switching of high-speed air-liquid two-phase flows using electrowetting-assisted flow-pattern change.

This work is the first demonstration of electrical modulation of surface energy to reversibly switch dynamic high-speed gas-liquid two-phase microfluidic flow patterns. Manipulation of dynamic two-phase systems with continuous high-speed flows is complex and interesting due to the multiple types of forces that need to be considered. Here, distinct stable flow patterns are formed through a multipronged approach: both surface tension forces generated by surface chemistry modulation as well as viscous and inertial forces produced by fluid flows are employed. The novel fluidic actuation mechanism provides insights into better understanding microscale two-phase flow dynamics and offers new opportunities for the development of two-phase biochemical microsystems that are mechanically simple and operational at high speeds.