With miniaturization of fluidic devices, small-scale effects such as the details of the flow near the contact line become important. We present a three-dimensional numerical model to simulate the dynamic behavior of moving contact line phenomena. The model consists of an adaptive mesh discretization of the time-dependent Navier-Stokes equations for incompressible two-phase flows with a volume-of-fluid technique for interface tracking. Equilibrium results of three-dimensional droplets with various contact angles are presented and compared with known solutions. The slip of a moving contact line on the solid surface and the dynamical contact angle are computationally investigated. Some numerical simulations of the model applied to electrowetting are presented.

Microfluidic devices are convenient for producing highly uniform droplets for precise emulsions and lab-on-a-chip devices. However, the minimum droplet size in a microfluidic process is determined by the smallest geometric feature size, typically on the order of tens of microns. Introducing additional physico-chemical effects can help overcome this fundamental limitation. For example, when dissolved surfactants are present in one of the liquid phases, a tipstreaming-like phenomenon occurs, leading to the formation of submicron droplets. We have characterized this phenomenon in detail as a function of fluid properties and flow kinematics. However, we still have only a phenomenological understanding of the role of surfactant in the tipstreaming process. Experiments and recent literature suggest that the adsorption and desorption of surfactants at the interface plays an important role. In this talk, we demonstrate the feasibility of this hypothesis via scaling arguments for the diffusion, adsorption, and desorption of soluble surfactants in micron-scale geometries.

We discuss an on-going theoretical / experimental effort studying particle separation through capillary electropohoresis in nanochannels. Recent experimental results in the laboratory of Dr. Pennathur (UCSB, Dept. ME) indicate that increased fidelity in separating particles by size and charge can be achieved when using channels with cross sections of nanometer dimensions (100nm x 1000nm) as opposed to larger microchannels. For short double-strands of DNA (10 - 100 base pairs) it is found that separation in free solution produces only one lumped peak in the fluorescence signal for microchannels but several clearly distinct peaks in nanochannels. Many effects which are weak in microchannels are expected to play a strong role in nanochannels owing to the large surface area to volume ratio and steric restrictions imposed on particle configurations. Models are presented for separation which investigate the role of the particle-particle and particle-wall steric interactions, the hydrodynamic flow and coupling, the overlap of double layers, and the translational and rotational diffusion of particles. This work is also being carried out with Dr. Gibou (UCSB, Dept. ME) and with the graduate student David Boy.

Self assembly is the idea of creating a system whose component parts spontaneously assemble into a structure of interest. In this talk I will outline our research program aimed at creating self-assembled structures out of very small spheres, that bind to each other on sticking. The talk will focus on (i) some fundamental mathematical questions in finite sphere packings (e.g. how do the number of rigid packings grow with N, the number of spheres); (ii) algorithms for self assembly (e.g. suppose the spheres are not identical, so that every sphere does not stick to every other; how to design the system to promote particular structures); (iii) physical questions (e.g. what is the probability that a given packing with N particles forms for a system of colloidal nanospheres); (iv) comparisons with experiments on colloidal nanospheres. and (v) ways of using microfluidics to enable kinetically driven self assembly.

Preprint (ArXiv)

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow.

We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features (1) significant salt depletion in the electrolyte near the electrodes and (2), at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell.

We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

Nanomechanical resonators enable a range of precision measurements in air or vacuum, but strong viscous damping makes applications in liquid challenging. Recent experiments have shown that fluid damping can be greatly reduced by confining the sample to a fluidic channel embedded inside the resonator while the outside is under vacuum. Understanding fluid damping in such systems is critical for future applications to problems spanning a wide range of scales in nanoscience and biology. Measurements presented here reveal that energy dissipation in cantilevers with embedded fluidic channels is a non-monotonic function of viscosity, suggesting that the quality factor may actually be enhanced through miniaturization. These results are found to be consistent with a first-order hydrodynamic model of the fluid-filled vibrating cantilever beam. In the regime of low-viscosity, inertia dominates the fluid motion inside the cantilever, resulting in thin viscous boundary layers - this leads to an increase in energy dissipation with increasing viscosity. In the high-viscosity regime, the boundary layers on all surfaces merge, leading to a decrease in dissipation with increasing viscosity. Effects of fluid compressibility also become significant in this latter regime and lead to rich flow behaviour. Based on these results, we anticipate that scaling of current devices by more than ten-fold may be possible without significant degradation of the quality factor due to damping induced by the fluid.

Keywords: electrokinetics, nanoscience, limiting current, Donnan potential, ion selectivity, Warburg Impedance

Abstract: With the advent of nanofabrication technologies, nano-channels with dimensions smaller than the Debye screening layer can now be fabricated to allow scrutiny of the various anomalous DC and AC I-V characteristics of ion-selective membranes at the single-pore level — such knowledge is essential for rapid DNA sequencing, single-molecule sensing/identification and plasmonic imaging in nanoscience. Combining theoretical analyses of the underlying ion/solvent fluxes and confocal imaging of velocity and ion concentration fields, we explore the fundamental mechanisms behind non-ideal selectivity, Donnan potential, asymmetric depletion/enrichment layer formation, limiting and overlimiting-current, diode-like rectification, Warburg impedance response, inter-channel communication etc. Curiously, hydrodynamic effects at the depletion end of the channel is found to control many of the non-Ohmic behavior at higher voltages. Interfacial vortices created by an osmotic pressure driven instability (first predicted by I. Rubinstein) and induced charges at the corners of nanopores are found to specify the overlimiting current, the rectification factor and inter-pore communication. The intensity of these vortices and their influence on the ion-carried currents are found to be strongly dependent on the pore/reservoir geometries and can be described by limiting fundamental solutions of the Laplace and Stokes equations due to severe electric and flow field focusing into the nanochannel.

The capillary-driven readjustment of thin liquid films subject to sudden, localized changes in shape or to periodic stretching of adjacent solid surfaces is important in a variety of industrial and physiological flow configurations. To investigate this process, we perform a combination of finite-difference numerical simulations and matched and multiple-scale asymptotic analyses of several related, simplified models. Thin films readjusting near isolated interior corners or "large" humps generically attain an intermediate-asymptotic state consisting of a corner puddle, a "Jones--Wilson" (or "Hammond") draining region, through which fluid slowly drains into the puddle, and a far-field, propagating capillary wave. (For thin-film flows near "small" humps, the capillary wave attaches directly to the hump.) In the presence of distant lateral no-flux boundaries, the thin film ultimately reaches a quasi-steady configuration consisting of a droplet, a Jones--Wilson draining region, and a corner puddle, as has long been known. This quasi-steady film distribution is dramatically altered by the introduction of prescribed substrate stretching. At low frequencies, the pressure distribution becomes non-monotonic and the drainage region is rendered passive. A "Bretherton" region, which connects the corner puddle to a wedge-like region emerges, and drag-out and drag-in profiles are asymmetric. At high frequencies, the effects of the pressure oscillation are screened in a small neighborhood of the corner. This work is motivated by applications in pulmonary alveolar mechanics.

An theoretical analysis is performed to explain recently observations that salt gradients across a nanopore can increase charged analyte capture rates.

Computational and theoretical models are developed for the transport of biomolecules and electrostatic and electrokinetic phenomena in nanopore membranes. For the application of nanopore sequencing, the electrophoretic transport of double stranded DNA molecules through a converging nanopore is investigated. The forces that affect the DNA translocation are analyzed and the DNA translocation velocity is predicted. The computational model is validated by good agreement between the computational results and the experimental data.

Motivated by the design requirements for a hemofilter in an implantable artificial kidney, the hindered transport of biomolecules through a nanopore membrane is studied, particularly for the selectivity of the charged membrane to charged biomolecules of biological interest, particularly human serum albumin. The developed theory is applied to the problem of choosing a hemofilter pore size that provides adequate retention/clearance of desirable/undesirable solutes from blood.

Keywords: Nematic Liquid Crystal, non-Newtonian, lubrication theory, asymptotics, electric field effects, interfacial instability, free boundary problem, LCD

Abstract: Nematic liquid crystals are materials intermediate between the liquid and solid states. They are typically composed of long, rod-like molecules, which have a tendency to align with their neighbors, imparting a short-range (but no long-range) orientational order - although nematics flow, like conventional liquids, they also retain some elastic character. This gives rise to complex behavior that does not arise in Newtonian liquids. Moreover, their response to an applied electric field gives nematics wide application in the electronic display industry.

We consider mathematical models for three different problems. Two are classical fluid-dynamical setups: a small droplet spreading on a flat substrate; and a two-dimensional "liquid bridge" (or liquid sheet) under tension. These are free boundary problems, and the thin geometry in each case enables the use of "lubrication" analysis to systematically derive reduced mathematical models governing the free surface evolution. The spreading drop analysis leads to variants of the classical 4th order "thin film" equation, which can exhibit instability in certain regimes. The "liquid bridge" problem leads to new versions of the so-called Trouton model for Newtonian viscous sheets.

The third problem arises in the display industry, and is concerned with manufacturing a "bistable" display device, that can exhibit two optically-distinct configurations in the absence of an electric field. Such a device has the potential for considerably reducing the power demands of a display, with accompanying benefits for battery lifetime and device portability.

We study the reaction diffusion equation u_t = u_xx + f(u), with a cut-off ε in the reaction term. The reaction term without a cut-off is assumed to be of KPP type. The introduction of the cut-off on the reaction term has been shown to model the effect of noise and the finiteness of the number of diffusing particles. Rigorous bounds on the speed are given for arbitrary values of ε. For small cut-off the Brunet-Derrida value is recovered, the bounds from allow to determine its range of validity. In the opposite limit of large cut-off the speed tends to zero as the square root of (1-ε). The results are obtained making use of a variational characterization of the speed.

Keywords: Brownian dynamics, microfabrication, boundary element method, DNA electrophoresis, separations

Abstract: I will present our recent results on the dynamics of long DNA as they move through a hexagonal arrays of microfabricated posts under the influence of an electric field. The first part of the talk focuses on the potential of using sparse, ordered post arrays to separate long DNA by molecular weight. In particular, I will focus on the crucial role of electric field gradients on the separation process and how we can use microfabrication tools to control these gradients. In the second part of the talk, I will demonstrate how we are using a combination of Brownian dynamics simulations and videomicroscopy to gain a detailed understanding of the separation process at the macromolecular level.

Keywords: DNA, microfluidic, nanofluidic, electrophoresis

Abstract: Large double stranded DNA are both a powerful system to study polymer dynamics at the single molecule level and also important molecules for genomic applications. While homogenous electric fields are routinely used to separate DNA in gels, DNA deformation in more complex fields has been less widely studied. We will demonstrate how micro/nanofluidic devices allow for the generation of electric fields with well-defined kinematics for trapping, stretching and then watching DNA relax back to equilibrium. The dimensions of the devices highly confine DNA and subsequently change both their conformation and dynamics. First, I will discuss how confinement changes the conformational relaxation time and introduces new relaxation regimes not seen in bulk. Next, I will show how these confinements effects change the coil-stretch transition of a DNA being electrophoretically stretched in a purely elongational electrical field.

Keywords: Singularities, Free surface flows

Abstract: Viscous flow is extremely effective in deforming a free surface into very sharp features such as tips or cups. Under increased driving such free surface singularities may turn unstable, and give way to secondary structures. In particular, this may be turned into a method to "manufacture" small things by using the nonlinear character of the equations of hydrodynamics.

We present thermodynamically consistent models for dynamic electrowetting and other electrokinetic phenomena involving conductive liquids or electrolyte solutions. They combine Navier-Stokes equations, evolution equations for ion/charge densities and for phase field with an elliptic transmission problem forthe electrostatic potential. We provide numerical and theoretical argumentsi ndicating that microscopically Young's contact angle persists in equilibrium configurations. Moreover, the models allow for contact-angle hysteresis. In addition, 2D and 3D numerical simulations on electric field induced droplet motion are presented. Finally, rigorous mathematical analysis shows global-in-time existence of solutions to the models under consideration.

Joint work with Paul Chiarot (Department of Electrical and Computer Engineering, University of Rochester).

In continuous ink jet systems, streams of ~10 picoliter liquid droplets (diameter ~30 microns) are ejected from an array of orifices at rates of up to 350,000 per second and velocities in excess of 20 m/s. Applications as diverse as printing, microfabrication, and microarraying benefit from this technology; however, reliable manipulation of the jet, including basic on/off control and steering of droplet streams and individual liquid droplets, remains difficult to achieve. We have developed a novel deflection scheme to manipulate the trajectories of droplets rebounding at shallow angles from a solid substrate based on the dielectrophoretic force exerted by patterned electrodes. Droplet rebound, key to the performance of this scheme, has been investigated for both fluorocarbon (Teflon) and superhydrophobic surface coatings. Our experiments reveal interesting droplet behavior, and at least two regimes of operation, that are dependent on the Weber number and on the properties of the solid surface with which the droplets collide and rebound.

This work was supported by a grant from Eastman Kodak Co. in Rochester, NY (USA).

Keywords: dielectrophoresis, electrowetting, electromechanics, microfluidics

Abstract: When subjected to electric fields, liquids exhibit a large range of dynamic and kinematic phenomena. This lecture focuses on the liquid electromechanical effects commonly exploited to dispense, move, and manipulate small liquid masses (including droplets) in microfluidic applications. Irrespective of the fine details, the net, observable force interaction very often can be predicted in terms of an appealingly simple, lumped parameter model. In particular, as long as the capacitance of a microfluidic structure can be expressed in terms of a small number of mechanical variables that adequately describe liquid displacement and distortion, then an electromechanical system model is born. Because such models can describe the important fluid behavior of insulating and conductive liquids, microfluidic schemes based on either liquid dielectrophoresis, electrowetting-on-dielectric, or a combination of the two can be treated. The lumped parameter approach avoids issues associated with volume force densities and often circumvents the need for numerical electric field computations.

The transport and dynamics of colloidal particles near a solid-liquid interface (i.e., the wall) is important in many microfluidic applications, including microscale particle-image velocimetry (PIV). Experimental studies using total internal reflection microscopy to study near-wall colloidal particle dynamics have for the most part only considered a single particle in a quiescent fluid. In contrast, our group has developed an evanescent wave-based technique that analyzes the dynamics of ensembles of up to O(10⁵) near-wall colloidal tracers, multilayer nano-particle image velocimetry (MnPIV). The technique exploits the exponentially decaying intensity of evanescent-wave illumination, to extracts near-wall particle distributions and flow velocities at different distances from the wall, all within about 500 nm of the wall. The technique has already been validated for steady and creeping Poiseuille flow, where the shear rates were found to be within about 5% of analytical predictions. In this study, we use MnPIV to investigate electrokinetically driven flows through fused-silica microchannels about 40 microns deep. The results for 100 nm to 500 nm diameter tracers show that the flows are uniform with constant electroosmotic mobility, and that the Brownian diffusion coefficients for tangential fluctuations are within 7% of the Faxén relation. The particle distributions near the wall are, however, in all cases, highly nonuniform, with very few particles within 100 nm of the wall due to electrostatic and van der Waals effects. Finally, the near-wall distribution of the 500 nm tracers are shown to vary with applied electric field, due presumably to dielectrophoresis and perhaps induced-charge electroosmosis.

The classical theory of a spherical colloids' electrophoretic mobility is founded on the Poisson-Nernst-Planck (PNP) equations and assumes the standard hydrodynamic no-slip boundary condition at the fluid/solid interface. In the (common) limit of thin double-layers, the mobility has long been known to exhibit a maximum at some zeta potential, then decrease and asymptote to a constant value. Dukhin, O'Brien, White and others showed this to result from the importance of excess ionic surface conductivity within the double-layer. The fundamental assumptions that underpin this result are, however, subject to challenge: in recent years, a finite liquid/solid slip has been measured over a variety of surfaces, and the PNP equations predict physically impossible ion concentrations precisely at the high zeta potentials where the mobility maximum occurs. Here, we discuss the dramatic effect that hydrodynamic slip and finite-ion-size steric effects in double-layers have upon the electrophoretic mobility of spherical colloids, and therefore upon the interpretation of electrophoretic mobility measurements.

We develop a theory on DNA electrophoresis that shows stretch-dependent electrophoretic mobility in agreement with an experiment observation. In our theory, a DNA molecule is modeled as a freely-jointed-chain, each of whose segments consists of a collinear series of charged spheres, which we call a "shish-kebab" segment. First, by calculating the interaction between charged spheres in an electric field, we show that the electrophoretic mobility of a shish-kebab segment is dependent on the orientation relative to the direction of the electric field. Then, the electrophoretic mobility of the whole DNA chain is evaluated by taking an ensemble average over the orientation of the shish-kebab segments in the chain. The result shows an enhancement of the magnitude of the electrophoretic mobility under the stretch of the DNA molecule.

Keywords: Wetting phenomena, surface domains, surface topography, contact line pinning, fluid membranes, vesicles, intrinsic contact angles

Abstract: Two types of wetting phenomena will be discussed: (i) Morphological wetting transitions at chemically patterned or topographically structured substrates; and (ii) Wetting of flexible membranes such as lipid bilayers by aqueous phases. Morphological wetting transitions between different droplet shapes occur, e.g., as one varies the amount of liquid deposited on the structured substrate. [1,2] The basic mechanism underlying this polymorphism is the freedom of contact angles at pinned contact lines. [3] The second system consists of lipid vesicles containing aqueous solutions with two species of water-soluble polymers. When the polymer concentrations are raised by deflation, the aqueous solution forms two coexisting liquid phases that may undergo complete-to-partial wetting transitions at the vesicle membranes. [4] Partial wetting is characterized by effective contact angles that can be measured by optical microscopy and by an intrinsic contact angle that represents a 'hidden' material parameter. [5]

[1] R. Seemann et al. PNAS 102, 1848 (2005) [2] P. Blecua, M. Brinkmann, R. Lipowsky, and J. Kierfeld. Langmuir (in press) [3] R. Lipowsky et al. J. Phys.: Condens. Matter 17, S2885 (2005) [4] Y.-H. Li, R. Lipowsky, and R. Dimova. JACS 130, 12252 (2008) [5] H. Kusumaatmaja, Y.-H. Li, R. Dimova, and R. Lipowsky. Phys. Rev. Lett. (submitted)

Keywords: Energetic Variational Approaches, ion channels, complex fluids

Abstract: Ion channels are key components in a wide variety of biological processes, such as nerve impulse, cardiac and muscle contraction, regulating the secretion of hormones into the bloodstream. Ion channels are a frequent target in the search of new drugs.

Ion channels, like enzymes, have their specific properties: potassium, sodium, calcium, and chloride channels allow only that type of ions to move through the pores. This selectivity is the key to all those biological process mentioned above.

Selectivities in both calcium and sodium channels can be described by the reduced models, taking into consideration of dielectric coefficient and ion particle sizes, as well as their very different primary structure and properties. The side-chains are represented only as charged spheres (calcium channel EEEA/EEEE; sodium channel DEKA). These self-organized systems will be modeled and analyzed with energetic variational approaches (EnVarA) that were motivated by classical works of Rayleigh and Onsager. The resulting/derived multiphysics-multiscale systems automatically satisfy the Second Laws of Thermodynamics and the basic physics that are involved in the system, such as the microscopic diffusion, the electrostatics and the macroscopic conservation of momentum, as well as the physical boundary conditions.

In this talk, I will discuss the some of the related biological, physics, chemistry and mathematical issues.

This is a joint work with Bob Eisenberg (Rush) and Yunkyong Hyon (IMA).

Joint work with Peichun Amy Tsai¹, Christophe Pirat¹, Alisia M. Peters², Rob Lammertink², Matthias Wessling², Sergio Pacheco³ and Leon Lefferts³.

The poster presents several different wetting phenomena on structured and unstructured superhydrophobic surfaces, namely (i) an evaporation triggered wetting transition, at which a drop on a structured surface jumps from the Cassie-Baxter state to the Wenzel state, (ii) a drop impact on carbon nanofiber jungles, for which eithers droplet rebound or splashes are achieved, depending on the impact velocity, and (iii) the measurement of the effective slip-length over micro-grooves through micro-PIV.

¹Physics of Fluids Group, ²Membrane Technology Group, ³Catalyst Materials and Process Group, University of Twente, the Netherlands

Keywords: inkjet printing, bubbles, drop formation, air entrainment, impact

Abstract: Piezo-acoustic inkjet printing has become a mature technique for high performance printing. Nevertheless, there are still various scientific challenges. In this overview talk I will cover some of them: (i) Coupling between the fluid dynamics and the acoustics, in particular when a disturbing bubble has been entrained in the ink channel. (ii) Optical and acoustical monitoring of the bubble. (iii) Mechanisms of the bubble entrainment. (iv) Droplet formation and pinch-off of droplets. (v) Droplet impact on substrates.

Main further contributors to the research: Jos de Jong, Roger Jeurissen, Arjan van der Bos, Michel Versluis, and the colleagues from Oce Technologies: Hans Reinten, Herman Wijshoff, and Marc van der Berg.

The dynamics of a lipid bilayer membrane is investigated in several different situations. Our model accounts for the transport of lipids along each monolayer, and intermonolayer friction, as well as the membrane fluidity and resistance to bending. First we consider a nearly-spherical vesicle in a shear flow. In this near-spherical limit we can reduce the model to a nonlinear coupled system of equations for the dynamics of the shape and the bilayer density difference. Multiple solution states are found as a function of viscosity ratio and the monolayer slip coefficient. Second, we investigate the stability of a planar membrane subjected to a DC electric pulse. The thin lipid membrane is impermeable to ions and thus acts as a capacitor. A linear stability analysis results in a time dependent system of equations for the growth rate as a function of wave number. Our theoretical findings are relevant to understanding the physical mechanisms of electroporation of biomembranes. Finally we discuss a novel computational method to determine the dynamics of a lipid bilayer vesicle in a viscous flow.

Keywords: Blood flow, microcirculation, modeling, rheology

Abstract: Various rich dynamics of vesicles under linear and nonlinear flows will be discussed. We present analytical and numerical results on tank-treading motion, tumbling and vacillating-breathing (aka swinging, trembling). We then discuss the notion of transverse migration due to a wall and to a nonlinear flow. We show theoretical and exeprimental results on the law of transverse migration in a microfluidic device. Finally, we present very recent results on a longstadning puzzle of the blood microcirculatory research: why do red blood cells adopt a non symmetric shape (called slipper) in small blood vessels?

A key result of our study is that the parachute symmetric shape is shown to be unstable, while the slipper shape is stable. That is, small flow disturbances–which are always present in real blood flows–cause RBCs to assume slipper shapes. It is further shown that the slipper shape offers a better transport efficiency to RBCs. In addition the slipper shape favors hemoglobin mixing in the cell, and thus enhances oxygen transport efficiency. Blood flow efficiency together with optimal oxygen supply seem to be determinant for natural selection of slipper shapes.

We present a simple analytical model that allows for determining the surface charge in electro-osmotic flow channels using the so-called solution displacement method. In contrast to earlier techniques, which have either been limited to small ratios of salt concentration or required a numerical solution of the convection-diffusion equation, our method provide a simple functional form with merely two fit parameters and thus allow for more accurate measurements of surface charge. Moreover, we demonstrate flow reversal inside our microfluidic channels controlled by gate electrodes underneath insulating layers that allow for external tuning of the surface charges. We discuss possible applications as a rheometer for applying shear forces to ultrasoft complex fluids.

Keywords: Electrowetting, mixing, electrothermal flow

Abstract: Mixing is a key issue in microfluidics, including droplet-based “digital” microfluidics. In electrowetting, internal flow patterns inside drops can be generated without any lateral translation if the drops are excited with AC voltage. Two regimes can be distinguished: at AC frequencies of the order of the eigenfrequency (typically O(1kHz) or less), the drops periodically oscillate between states of high and low contact angle. Despite the periodicity, there is a symmetry breaking in the drop shape between the spreading and the receding phase, which causes a time-averaged net flow inside the drop that promotes mixing. This process can be described using a model based on capillary wave-driven Stokes drift. For somewhat higher frequencies, this mechanism becomes progressively inefficient, because the liquid cannot follow the applied voltage anymore. At substantially higher AC frequencies (typically >>10kHz, depending on the salt concentration), however, a new driving mechanism for internal flows sets in, as reported by Nichols and Gardniers (Anal. Chem. 79, 8699 (2007) and by Ko et al. (Langmuir 24, 1094, 2008). Under these conditions, the liquid no longer acts as a perfect conductor. The electric field penetrates into the drop and generates local Ohmic currents. These currents produce Joule heating and ultimately giving rise to electro-thermal flows inside the drops. Solving numerically for the distribution of the electrostatic field, the flow field, and the temperature distribution, we show that the flow velocity scales with the fourth power over a wide range of both the applied voltage and the AC frequency – in good agreement with the experiments by Ko et al.

Boundary integral methods are computationally efficient in computing the evolution of interfaces in Stokes flow. For axisymmetric interfaces, they reduce to evaluating a 1d integral at each time step. We have performed a detailed analysis of the structure of the integrands and show that standard methods of integration present two difficulties. One arises from loss of precision due to cancellation, the other from singular behaviour of the integrands near the axis of symmetry. As a result, high order quadrature proposed previously for these types of integrals are not uniformly high order. Instead, the maximal errors are always of second order. We propose a remedy to both difficulties and present a uniformly accurate 5th order approximation. This new quadrature is implemented to evolve (1) an initially bar-belled bubble that pinches at a point in finite time, and (2) a sphere in a strain flow that approaches a steady state. We compare the results with commonly used second order approximations and show that significant improvement is obtained using 5th order rules. The examples also illustrate when the corrections needed for uniformity have an impact in practice.

Keywords: shear banding, boundary conditions, flow instabilities, wormlike micelles

Abstract: Shear banding fluids such as wormlike micelles, lamellar surfactant solutions, and emulsions, undergo "transitions" between fluids of different apparent viscosity as a function of applied flow conditions. This switching makes them appealing for use in microfluidic applications. Since their physics is controlled by the influence of flow on internal microstructure, which in turn is influenced by boundary effects, it is important to develop an understanding of how different kinds of boundary effects influence shear banding. In this talk I will discuss some of these issues, mainly using constitutive models inspired by experiments on wormlike micelles or polymer solutions. and explore the effects of different boundary conditions for the additional viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. I will note some of the features expected to be important for microfluidic geometries.

[Work done in collaboration with JM Adams and SM Fielding]

Keywords: electrokinetics, nanofluidics, possion-boltzmann, TIRFM

Abstract: The advent of nanofabrication technologies allows for the development of robust nanoconfined fluidic channels. In this talk I will outline some recent advances and challenges in our research program aimed at elucidating linear and nonlinear electrokinetic phenomena within such channels. First, I will present a combined theoretical and experimental study of the dissolution of fused silica nanofluidic channels when subject to pressure driven flow of aqueous solutions. Time sensitive current measurements within these channels allow for determination of the dissolution rate from the classic linear Poisson-Boltzmann equations for fluid flow and Gouy-Chapman-Stern-Grahame charge regulation model for the surface boundary conditions. Next, I will describe a novel total internal reflectance microscopy (TIRFM) system we have developed and recent experimental results towards to the elucidation of coupled nanofluidic electrokinetic systems, namely, the addition of finite sized charged quantum dots and/or biomolecules on the order of the size of the channel. Finally, I will discuss some experimental nonlinear electric-field dependent phenomena observed around metal electrodes within a nanofluidic channel.

At ASU, we are investigating locomotion of bimetallic synthetic nanomotors that, analogous to their biological counterparts, harvest chemical energy from their local environment and convert it to useful work. Bimetallic nanorods can autonomously propel themselves at a hundred body lengths per second through aqueous solutions by using hydrogen peroxide as a fuel. Magnetic fields and electrochemically induced chemical species are used to control the motion of Pt-Ni-Au nanorods. We use the magnetic properties of nickel-loaded nanomotors to control their motion through micron-scale structures as well as the loading, transport, and release of spherical cargo that have volumes two orders of magnitude larger than the nanomotors itself. Nanomotor locomotion forces are determined by measuring their velocity while towing spherical cargo that have Stokes drag eight times the nanomotors themselves.

Several physical arguments have been proposed to describe the physics underlying chemically-powered locomotion, but there is no detailed theory on the propulsion mechanism. We are simulating the physics of rod-shaped nanoparticles with asymmetric surface fluxes. Our models show that locomotion is driven by electric body forces in the fluid that arise due to finite space charge and internally generated electric fields surrounding the rod. The electric fields and charge density are generated by dipolar cation fluxes, such as those generated by heterogeneous electrochemical reactions with broken symmetry. The scaling analysis and detailed simulations predict that the nanomotor velocity depends on the reaction flux, nanorod electrical surface potential, solvent viscosity, and rod geometry.

Our interests lie in exploiting physical fluidic mechanisms to program and control matter at small length scales. In the first part of the talk, I will describe a novel way to employ physical computation to build all-fluidic control circuits. I will introduce how to build both "analog" and "digital" circuits that can implement universal Boolean logic, feedback, cascadability, bistability and synchronization via exploiting purely hydrodynamic nonlinearities in low-Reynolds number multi-phase flow. These circuits provide a means to control sub-nanoliter droplets in fluidic channels up to KHz regime with no moving parts.

In the second part of the talk, I will describe techniques for in-situ synthesis of morphologically diverse nanostructures via geometrical control. By physically coupling growth and transport dynamics of reactants in a continuous flow reactor, we demonstrate programmed synthesis of complex geometrical patterns of Zinc Oxide nanowires in microchannels. Time permitting, I will discuss some of our on-going work on development of new tools for stretching biomolecules.

Since Worthington, many situations generated by impacts in liquids were documented and explored. In this spirit, we would like to present several recent observations related to the behavior of projectiles after they hit different kinds of liquids. We first discuss the impact on soap films, and naturally extend these observations to foams, focussing on the ability of such complex fluids to absorb the kinetic energy of the projectiles. We also consider impacts in a viscous liquid, and describe the particular kind of cavity generated by the shock. And we conclude by looking at the behaviour of revolving projectiles, discussing the characteristics of the trajectory induced by the rotation.

Other contributors to this talk: Anne Le Goff, Guillaume Dupeux and Christophe Clanet.

Pumping of electrolytes in microchannels can be achieved with arrays of microelectrodes subjected to AC potentials. Here we show experiments on electrolyte flow induced by microelectrodes subjected to traveling-wave potentials. For sufficiently high voltages, Faradaic currents are present, leading to changes in the liquid properties and, in particular, changes in pH. A remarkable feature of the observations is that at voltages above a threshold, the direction of the fluid flow is reversed.

These observations motivate the theoretical study of Faradaic currents in electrokinetics for the general case of ionic species with different mobilities. We find, using a linear analysis, that the structure of the electrical double layer (EDL) has to be extended. The EDL consists of the compact and Debye layers, as in previous models, plus a diffusion layer that arises as a consequence of Faradaic currents. For the general case of different mobilities, there is a net electrical charge associated to the diffusion layer. As a particular result of this model, we show that traveling potentials generate flow in the reverse direction for the case of a thick compact layer and facile Faradaic reactions, if the reacting ions are the more mobile. This situation is consistent with the experimental observation of changes in pH due to proton reactions at the electrodes.

Keywords: Extended Space Charge, Concentration Polarization, Overlimiting Conductance, Nonequilibrium Electroosmotic Instability

Abstract: Our talk is about ionic currents from an electrolyte solution into a charge selective solid, such as, an electrode, an ion exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization – formation of solute concentration gradients under the passage of a DC current. We start by reviewing a few seemingly different phenomena occurring in that range. These are anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, over-limiting conductance in electrodialysis and the recently observed non equilibrium electroosmotic instability. All these phenomena result from formation of an additional extended space charge layer next to that of a classical electric double layer at the solid/liquid interface. We review the peculiar features the extended space charge and their relation to the mechanisms of the above mentioned phenomena.

Neuro-chips (NCs) are bio-hybrid devices in which living brain cells and silicon circuits are coupled together. NCs are presently being used as a non-invasive technique to record cellular response to drugs, and are expected to be used in the cure of neurological disorders through the creation of sophisticated neural prostheses. The main technological challenge in the design of NCs is the efficient transduction of the input biological signal (ion current of the order of nA) into an output signal (electrical current) which is modulated by the effective driving voltage of the open Gate of the silicon device (of the order of mV). In order to devise a sound simulation tool of the I/O behavior of a NC device, we propose a multi-physics computational model including: 1) the Poisson-Nernst-Planck system, to account for intracellular and extracellular electrochemical ion transport; 2) the Hodgkin-Huxley system, to describe ion transport across membrane channels; 3) a nonlinear MOS capacitor approximation, to account for cell-to-chip coupling. The nonlinear system arising from the coupled solution of 1)-3) is successively solved by a functional iteration procedure, and for each time level of the simulation, each obtained sub-problem is numerically solved using a stabilized mixed-hybridized finite element discretization scheme. In order to provide a successful validation of the computational procedure, we discuss preliminary results on two cases of physiological interest, namely, the Hodgkin-Huxley axon and the response of a field-effect transistor with metal-free gate oxide under an intracellular voltage depolarization stimulating impulse.

The ability to trap individual particles, cells and macromolecules has revolutionized many fields of science during the last two decades. Several methods of particle trapping and micromanipulation have been developed based on optical, magnetic and electric fields. In this work, we describe an alternative trapping method, the hydrodynamic trap, based on the sole action of hydrodynamic forces in a microfluidic device. A microfluidic cross slot device is fabricated consisting of two perpendicular microchannels where opposing laminar flow streams converge. In this device, a purely extensional flow field is created at the microchannel junction, thereby resulting in a semi-stable potential well at the stagnation point which enables particle trapping. We implement an automated feedback-control mechanism to adjust the location of the stagnation point which facilitates active particle trapping. Using the hydrodynamic trap, we successfully demonstrate trapping and manipulation of single particles and cells for arbitrarily long observation times. This technique offers a new venue for observation of biological materials without surface immobilization, eliminates potentially perturbative optical, magnetic and electric fields, and provides the capability to change the surrounding medium conditions of the trapped object during observation.

Keywords: Brownian rods, surfboards, drug delivery, capsules, vesicles, margination

Abstract: Many dispersions of colloidal particles with application in materials processing, biological assays, or medicine, contain elongated particles (e.g. ellipsoidal disks, rods, etc.) Recently these particles have been used in drug delivery applications because of the inability of leukocytes to easily rid them from the circulation. Moreover such particles are useful at the nanoscale for application in cancer therapies, either for detection of tumor vasculature or for the delivery of anti-cancer agents to tumor endothelial cells. Thus, the study of anisotropic particulate flows with adhesion in microchannels especially in mixtures with vesicle flows (i.e. red blood cells) has taken on a particularly important set of engineering applications. In order to understand the transport in these systems, a numerical simulation must include: a) a high fidelity representation of nonequilibrium dynamics of vesicles and capsules in microflows, b) the dynamic simulation of Brownian colloidal particles of general shape in microflows, and c) the combination of these in mixtures at finite concentration. Each of these transport processes brings in new physics which we will review. In discussing a) we will focus on the transition between tank-treading, tumbling, and trembling dynamics in flow and whether these transitions also happen at finite concentration in microfluidics. In b) we will discuss the particle concentration distribution of Brownian nonspherical particles in microfluidic flows and its relation to the nonequilibrium osmotic pressure. In c) we will examine how particle margination in mixtures occurs and how it is related to the concentration of vesicles/capsules in the microflow. Ultimately, we will look toward the virtual prototyping and engineering of these therapies.

Keywords: Streaming potential, multiphase flow, porous media

Abstract: Streaming potentials generated by single phase flow are reasonably well-understood, but much less is known about the effects of multiphase flow. The introduction of a second fuid phase can either increase the wall shear rate (thereby increasing streaming currents caused by convection of ionic charge clouds), or can decrease it, depending on the ratio of the viscosities of the two phases and on the effect of interfacial tension. If the second phase is non-conducting (e.g. oil droplets in water), the effective conductivity of the mixture is decreased, and streaming potentials tend to increase. I shall review the few experimental results that are available, and describe recent theoretical work aimed at understanding the effect of a single particle or fluid droplet flowing through a capillary.

J.D. Sherwood, Streaming potential generated by two-phase flow in a capillary. Phys. Fluids, 19 (2007) 053101.

J.D. Sherwood, Streaming potential generated by a long viscous drop in a capillary. Langmuir, 24 (2008) 10011.

E. Lac & J.D. Sherwood, Streaming potential generated by a drop moving along the centreline of a capillary. J. Fluid Mech. (in the press)

Keywords: nanofluidics, channel, diode, ion current

Abstract: Transport through nanopores and ion channels exists in virtually all biological cells and is important in such things as the regulation of heart function, nerve signals, and delivery of nutrients to the cell. Nanopores have also started to play a major role in contemporary biotechnology, because many separation and sensing processes require pores with nanometer-sized openings. My scientific interests have been focused on fabricating synthetic single nanopores with applications in biophysics and nanotechnology. The nanopores that we fabricate by the track-etching technique have diameters as small as 1 nanometer, they have controlled geometry and surface chemistry. I will show application of these nanopores as devices for controlling the flow of ions and charged molecules in a solution, functioning as ionic bipolar and unipolar diodes as well as ionic transistors. These functions are achieved by patterning the surface charge of the pore walls. Our systems will be applicable in nanofluidic, lab-on-the-chip, and biosensing systems. An example for application of ionic diodes in building sensors for anthrax will be discussed. I will also show how to induce ion current oscillations in time with frequencies between tens of Hz and fractions of Hz.

Electroosmosis, originating in the Debye-layer near the solid/liquid boundary within a fully-saturated porous substrate, can pump successfully against the capillary pressure arising from the surface tension of a droplet placed in series with the pump. As droplet size diminishes, the voltage required to pump electroosmotically down-scales favorably. The technological implication is that electromechanical transducers made of large arrays of small droplets, so-called 'droplet micro-manipulators', and Debye-layer 'diagnostic machines', inferring zeta-potential by measuring interface deflection of a droplet-pump-droplet configuration, become feasible. These applications will be illustrated and we will describe the current modeling of such multi-scale interfacial systems, highlighting open questions that might benefit from an applied mathematical approach.

Nanofluidic devices with an embedded nanotopography direct the self-organization and transport of long DNA molecules by influencing the free energy landscape. We studied the pressure-driven transport of DNA in slit-like nanochannels containing linear arrays of nanopits. We imaged individual DNA molecules moving single-file down the nanopit array, undergoing sequential pit-to-pit hops using fluorescence video microscopy. Distinct transport dynamics were observed depending on whether a molecule could occupy a single pit, or was forced to subtend multiple pits. We interpret these results in terms of a scaling theory of the free energy of polymer chains in a linear array of pits. Molecules contained within a single pit are predicted to face an entropic free energy barrier, and to hop between pits stochastically by thermally activated transport. Molecules that subtend multiple pits, on the other hand, can transfer DNA contour from upstream to downstream pits in response to an applied fluid flow, which lowers the energy barrier. When the trailing pit completely empties, or when the leading pit reaches its capacity, the energy barrier is predicted to vanish, and the low-pressure, thermally activated transport regime gives way to a high-pressure, deterministic transport regime. These results contribute to our understanding of polymers in nanoconfined environments, and can guide the design of nanoscale lab-on-a-chip applications for DNA analysis.

We present an diffusive interface approach to modeling multi-phase flows. A modified interfacial energy functional is employed to describe diffusive interfaces of (im)miscible phases. A fluid system where the Stokes equations are coupled with convection-diffusion equations are derived from the energy functional via the Energetic Variational Approaches (EVA). A particular case with slip boundary conditions on the interfaces were studied. In the numerical simulations we applied the Pressure Schur Complement (PSC) method to the hydrodynamical system. A Krylov subspace method with an Algebraic Mutligrid (AMG) preconditioner was used to solve the resulted linear system.

The complex interplay of electrophoretic, electroosmotic, bulk convective, and diffusive mass/charge transport in a hybrid poly(dimethylsiloxane) (PDMS)/glass microchannel with embedded floating electrode is analyzed. The thin floating electrode attached locally to the wall of the straight microchannel results in a redistribution of local field strength after the application of an external electric field. Together with faradaic reactions taking place at the bipolar electrode and buffer reactions, as well as bulk convection based on cathodic electroosmotic flow, an extended field gradient is formed in the anodic microchannel segment. It imparts a spatially dependent electrophoretic force on charged analytes and, in combination with the bulk convection, results in an electric field gradient focusing at analyte-specific positions. Analyte concentration in the enriched zone approaches a maximum value which is independent of its concentration in the supplying reservoirs. A simple approach is shown to unify the temporal behavior of the concentration factors under general conditions.

Drop deformation in uniform electric fields is a classic problem. The pioneering work of G.I.Taylor demonstrated that for weakly conducting media, the drop fluid undergoes a toroidal flow and the drop adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed a nonaxisymmetric rotational mode for drops of lower conductivity than the surrounding medium, similar to the rotation of solid dielectric spheres observed by Quincke in the 19th century.

I will present an experimental and theoretical study of this phenomenon in DC fields. The critical electric field, drop inclination angle, and rate of rotation are measured. For small, high viscosity drops, the threshold field strength is well approximated by the Quincke rotation criterion. Reducing the viscosity ratio shifts the onset for rotation to stronger fields. The drop inclination angle increases with field strength. The rotation rate is approximately given by the inverse Maxwell-Wagner polarization time. We also observe a hysteresis in the tilt angle for low-viscosity drops.

I will also discuss our work on drops encapsulated by complex interfaces such as lipid bilayer membranes. A comparison between the behavior of drops and giant vesicles (cell-size lipid membrane sacs) highlights new features due to the membrane electromechanics.

This work is in collaboration with Paul Salipante (Dartmouth) and Dr. Rumiana Dimova’s group (Max Planck Institute of Colloids and Interfaces).

An ideally polarizable cation-selective solid particle is suspended in an electrolyte solution and is exposed to a uniformly applied ambient electric field. The electrokinetic transport processes are described in a closed mathematical model, consisting of differential equations, representing the physical balance laws, as well as boundary conditions and integral constraints, representing the physicochemical condition on the particle boundary and at large distances away from it. Solving this model would in principle provide the electro-kinetic flow about the particle and the concomitant particle drift relative to the otherwise quiescent fluid.

Using matched asymptotic expansions, the model is analyzed in the thin-Debye-layer limit. An effective `macroscale' description is extracted, whereby effective boundary conditions represent appropriate asymptotic matching with the Debye-scale fields. The macroscale description significantly differs from that corresponding to a chemically inert ideally polarizable particle. Thus, ion selectivity on the particle surface results in a macroscale salt concentration polarization, whereby the electric potential is rendered non-harmonic. Moreover, the uniform Dirichlet condition governing this potential on the particle surface is transformed into a non-uniform Dirichlet condition on the macroscale particle boundary. The Dukhin--Derjaguin slip formula still holds, but with a non-uniform zeta potential that depends upon the salt concentration distribution.

For weakly applied fields, an approximate solution is obtained as a perturbation to an equilibrium state. The linearized solution corresponds to a uniform zeta potential; it predicts a particle velocity which is proportional to the applied field. The associated electrokinetic flow differs however from that in the comparable electrophoresis of an inert particle surface, since it is driven by two different agents, electric field and salinity gradients, which are of comparable magnitude. The velocity field, specifically, is rotational.

Keywords: Interfacial particle-image velocimetry, colloidal particles, microfluidics, electrokinetically driven flows

Abstract: Interfacial effects are important in many cases for microscale transport. One of the few experimental techniques that can resolve interfacial transport with sub-micron spatial resolution is evanescent wave-based, or nano-, particle-image velocimetry (PIV), which determines fluid velocities over the first 500 nm next to the wall from the displacements of 100-500 nm neutrally buoyant tracers. The wall-normal spatial resolution of nano-PIV is further improved by multilayer nano-PIV (MnPIV), which exploits the exponentially decaying intensity of evanescent-wave illumination to obtain velocities at different distances from the fluid-solid interface within about 500 nm of the wall. In agreement with DLVO theory, the distribution of the colloidal tracers within a particle diameter of the wall measured by MnPIV is highly nonnuniform due to repulsive electric double layer interactions and van der Waals effects. Nevertheless, the MnPIV results for steady creeping Poiseuille flow are in good agreement with analytical predictions once the velocities have been corrected for this nonuniform distribution. This talk describes velocity and Brownian diffusion coefficient measurements obtained from tracers with diameters ranging from 100 nm to 500 nm for Poiseuille flow through hydrophilic and hydrophobically coated fused-silica microchannels and for electrokinetically driven flows through fused-silica microchannels with a minimum cross-sectional dimension of about 40 microns. The near-wall particle distributions for 500 nm tracers are shown to vary with electric field for the electrokinetically driven flows, due presumably to electrophoresis and induced charge electroosmosis.

We examined the important over-limiting ionic current phenomenon, occurring at ion-permselective nanoporous membrane or nanochannel, and suggested a modified theoretical description of the entire nonlinear current-voltage curve based on the instability selected concentration-polarization layer thickness. In the process we discovered several curious and non-intuitive behaviors: 1) a nanoslot array with a uniform surface charge and height but with asymmetric slot entrances is shown to exhibit strong rectification, gating type current-voltage characteristics and a total current higher than the sum of isolated slots at a large voltage; 2) the vanishing of the limiting resistance voltage window with increased geometrical field focusing effect obtained by varying the nanoslot width. Hence, suggesting that an optimal pore radius/separation ratio exists for maximum current density across a membrane; 3) strong nanocolloid-nanoslot interaction that leads to an additional transition region (or critical voltage) prior to the overlimiting region.