Microfluidic Transport Based on Surface Directed Flows
An ever growing number of studies involving bacterial, cell or genomic assays rely on miniaturized diagnostic platforms known as labs-on-a-chip. These devices are being used both for fundamental research and commerical applications. Microfluidic chips, which typically require much smaller sample sizes than conventional diagnostic systems, allow for precise control over the spatial and temporal distribution of flow speeds as well as the concentration of nutrients, catalysts, competitor colonies, etc. The majority of such devices use pressure or electric field gradients to generate internal flow within enclosed microchannels. In contrast, our laboratory has been exploring a number of alternative driving mechanisms for generating the flow of thin liquid films or droplets along flat or curved surfaces in an open geometry. Surface directed or "open architecture" flows can be achieved by activated gradients in temperature, concentration, electric, magnetic or acoustic fields or by selective actuation of adjacent boundary motion. In this way, surface stresses generated at air-liquid, liquid-liquid or liquid/solid interfaces can be used to tune the shape and speed of stationary or moving liquid elements. The capability to tailor the shape of micro- or nanoscale liquid structures introduces a wealth of applications for biofluidic and optofluidic applications including the design of various nanowell channels as well as tunable filters, gratings, waveguides and photonic structures.
 
Microfluidic Chip Based on Thermocapillary Actuation
We have developed a microfluidic chip which combines thermocapillary stresses with selective substrate patterning to guide and tune the flow of liquid samples along the surface of a substrate. By controlling the voltage applied to embedded thin metal film heater arrays, we can selectively apply on demand specific temperature distributions with high spatial resolution. The local thermal gradients alter the surface tension of the adjacent liquid sample thereby inducing thermocapillary stresses which propel the liquid away from warm regions and toward cooler regions of the substrate. The liquid surface temperature can also be tuned by varying the intensity of radiative heating of the air-liquid interface using an overhead laser and programmable mirror array. With either method, the liquid flow speed and direction of liquid trajectories can be electronically tuned. We have used this device as a miniature automated platform for such functions as a droplet router for polar and organic liquids, droplet trapping and release, droplet scission, controlled sample mixing, and monitoring of chemical reactions. What makes this technique particularly attractive for microfluidic applications is the variety of tasks possible solely by control of the liquid surface temperature. These experimental studies are also complemented by an extensive theoretical program which includes hydrodynamic modeling as well as molecular dynamics simulations.
 
Microfluidic Detection and Analysis by Integrated Evanescent Wave Sensing
Our laboratory has previously demonstrated two methods for droplet detection and sensing for microfluidic devices which makes use of the coplanar microelectrode arrays used for thermocapillary actuation. The first method monitors the thermal rise time of embedded microheaters, from which can be extracted droplet location, volume or composition due to changes in thermal conductivity induced by the presence of overlying liquid film. The second method records the capacitance change induced by an overlying droplet. Rapid response for electrode widths which are comparable to the liquid film thickness allows for accurate detection of droplet position, volume, composition and evaporative loss even for nanoliter liquid samples. These sensing techniques, which probe samples by thermal or electric fields, however, are not suitable for all applications. In this respect, integrated optical and spectroscopic probes, such as evanescent sensing, offer significant advantages over these diagnostic techniques.
 
In a recent set of experiments, we have demonstrated a non-intrusive optical method for microfluidic detection and analysis based on evanescent wave sensing. The device consists of a planar thin film waveguide integrated with a microfluidic chip based on thermocapillary flow. Microliter droplets are electronically transported and positioned over the waveguide surface by actuation of a glass-embedded microelectrode array. The attenuated intensity of propagating modes is used to detect droplet location, to monitor dye concentration in aqueous solutions, and to measure the increase in chemical reaction rates as a function of increasing substrate temperature for a chromogenic biochemical assay. This study illustrates just a few of the capabilities possible by direct integration of optical sensing with surface directed fluidic devices. Our design also offers high sensitivity with few additional fabrication steps and is especially well suited to any fluidic device based on droplet manipulation by modulation of surface tension. We are currently investigating alternate substrate structures which offer the possibility of increasing the evanescent field intensity by one to two orders of magnitude useful for increasing the sensitivity and specificity of this device.
 
High Resolution Lithography by Microscale Contact Printing
Large area electronics such as light emitting displays require far less stringent resolution limits than conventional photolithography. The demand for applications with lower resolution has triggered the development of patterning and fabrication methods which are large area, high throughput and low cost. We have demonstrated that contact printing methods like offset and letterpress methods when scaled down to the microscale can be used to produce wet and dry etch resist masks of arbitrary shape and thickness on flat or spherical surfaces. These structures can be fabricated cheaply and rapidly yet accommodate wide area formats containing disparate sizes and shapes. Recently, our lab has demonstrated that polymer etch masks printed with a microscale letterpress stamp can be used to fabricate amorphous thin film transistors with I-V curves comparable to those fabricated by conventional photolithography. This study, which focuses on flexible electronics, also includes a significant modeling effort based on energy minimization and fluid dynamical studies designed to parametrize and optimize the flow and surface conditions required for various stages of the printing process.
 
Phase Transitions and Broken Symmetry in Nanoscale Bilayer Films
Freely suspended bilayer films consisting of mobile, charged self-assembling "walls" of surfactant monomers, which can undergo exchange with micelles and polymer molecules in the bulk, are ubiquitous in nature and form the essential ingredients of soap films, tear films in the eye and even cell membranes. At wall separation distances in the nanometer range, these films become subject to an oscillatory disjoining pressure which causes thinning transitions between metastable states called layering transitions. Studies of 2- or 3- component liquid films containing micelle-polyelectrolyte or micelle-polymer complexes reveal that the discrete jumps in film thickness correlate closely with the characteristic size of micelles or the micelle-polymer coil size, respectively. Measurements by other groups by a thin film pressure balance or laser light scattering have confirmed that discrete layers of fluid can be successively expelled due to an interaction potential stemming from van der Waals, electrostatic and hydration forces.
 
Our investigations of the dynamics of freely suspended, bilayer nanoscale films containing micelle-polymer complexes (whose characteristic size is larger than the confining dimension) have revealed two novel instabilities. Video microscopy of film thinning toward the final metastable state has revealed spontaneous nucleation of a microdomain phase that rapidly permeates the surrounding thicker film. The rapidly expanding perimeter of these microdomains, however, is not circular or elliptical as common in similar systems without complexation, but develops a highly ramified front whose fractal dimension correlates strongly with the liquid viscosity. Despite that the surfaces of the freely suspended film are highly mobile and not confined between rigid walls, the lateral growth of this distinct phase shows striking resemblance to the Saffman-Taylor instability in macroscale systems. For sufficiently high polymer molecular weight, the permeating phase undergoes a secondary instability that generates a densely packed array of flattened nanodroplets whose packing density within the fractal perimeter exhibits 4-fold symmetry. This reduced symmetry stands in sharp contrast to the usual hexagonal packing structure observed in conventional simple fluid or colloidal systems. We are investigating these and similar systems in order to understand how nanoconfinement between deformable or soft interfaces can trigger phase transitions whose moving boundaries undergo rapid shape transformations toward dynamic fractal structures.
 
Slip Boundary Conditions for Liquid-on-Solid Flows
The development of micro/nanofluidic devices for liquid films, droplets or bubbles requires detailed knowledge of the interfacial forces and boundary conditions governing transport phenomena at small length scales. The celebrated no-slip condition used to calculate velocity and stress profiles in hydrodynamic flows dictates that a liquid element adjacent to a solid surface must equal the velocity of that surface. Despite its simplicity, this boundary condition has proven remarkably successful in reproducing most commonplace flows. There exist, however, notable examples for which this boundary condition leads to a divergence in the viscous shear stress. Examples include the spreading of a liquid drop on a solid substrate and the extrusion of polymer melts from a capillary tube.
 
It is now well accepted that suitably constructed boundary conditions which allow fluid elements to slip past the adjacent solid surface can regularize such flows and reproduce realistic behavior. Unfortunately, these slip models are phenomenological in origin and provide no universal understanding of the nature of momentum transport at liquid/solid interfaces. Using molecular dynamics simulations of liquids in planar shear, we have shown there exists a general non-linear function relating the slip length to the local shear rate along smooth or roughened liquid-solid interfaces. We are also currently investigating observed deviations between the predictions of molecular dynamics simulations and continuum (hydrodynamic) studies of nanoscale liquid films in planar shear to establish how the local shear rate, liquid structure factor, wall roughness and variations in wall surface energy affect the degree of slip in non-inertial flows. These deviations offer insight useful to the development of multiscale models.
 
Evolution of Digitated Structures in Marangoni Driven Flows
The spreading of a surfactant coated droplet on a thin liquid film of higher surface tension is known to produce an unusual fingering instability near the initial deposition edge. The spreading front undergoes repeated branching and tip-splitting forming arterial or dendritic patterns characterized by a fractal dimension similar to processes governed by Laplacian growth. Calculations based on linear stability and transient growth analysis suggest that the coupling of Marangoni and capillary stresses causes dramatic variations in film thickness and surfactant concentration which rapidly destabilize the advancing front. Interestingly, this system of coupled PDEs is unique in that the corresponding disturbance equations harbor the potential for large transient growth despite that the flow is well characterized as a lubrication type flow for which the Reynolds number plays no role. We are currently conducting experimental and theoretical studies to identify the characteristics of the base state profiles and conditions leading to instability to identify the source of unstable flow in sufficiently thin films. This problem of a surfactant monolayer spreading on a thin liquid film is of relevance to the study of certain respiratory diseases in newborn infants, which are alleviated by the exogenous delivery of lung surfactant. While many studies have focused on the equilibrium properties of the formulations used in clinical applications, our laboratory focuses instead on the dynamics of the spreading process in order to prevent non-uniform coverage of the surfactant concentration.
 
Most recently, we have used refracted Moire topography to reconstruct the spatial and time dependent waveforms associated with the spreading dynamics of a model lipid monolayer. This system closely mimics the behavior of an insoluble surfactant driven to spread on a thin viscous layer under the action of Marangoni stresses induced by variations in surfactant concentration. The film thickness profiles exhibit a strong surface depression ahead of the surfactant source capped by an elevated rim at the surfactant leading edge. The surface slope and shape as well as the propagation speed of the advancing rim are directly compared with numerical solutions of a lubrication model based on Marangoni driven spreading of a surfactant monolayer. Comparison between the theoretical and measured profles reveals the importance of the initial shear stress in determining the evolution in the film thickness and surfactant distribution. This initial stress appears to thin the underlying liquid support so drastically that the surfactant droplet behaves as a finite and not an infinite source even though there is always present an excess of surfactant at the origin.
 
Moving Front Instabilities in Film Spreading Driven by Surface or Body Forces
When a thin liquid film is forced to wet and coat a solid surface by the application of a body or surface force, the advancing front can develop a narrow capillary ridge at the leading edge of the film. This ridge is highly unstable and easily separates into numerous parallel rivulets which act as channels for the flow. Examples of this instability include liquid paint streaming down a vertical wall, the spin coating of a liquid film on a rotating substrate, the thermocapillary migration of a liquid film on a differentially heated substrate, or the forced spreading of a viscous film by an overhead gas stream. We have investigated these types of fingering instabilities via modal and transient growth analysis. For the thermocapillary driven system, the optimal perturbations which give rise to the fingering behavior rapidly asymptote to the most unstable modes determined from linear stability of the base state traveling wave solution. This holds true even if the base state equation includes van der Waals interactions. Our work provides the basis for understanding the excellent agreement between experiment and linear stability theory despite the non-normal character of the relevant disturbance matrix. We are extending our studies to other coating flows and to surfaces of mixed wettability obtained by chemical micropatterning.