Sandra M. Troian

A general boundary condition for liquid flow at solid surfaces

Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate, corner flow and the extrusion of polymer melts from a capillary tube. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.

Fingering Instabilities of Driven Spreading Films

We show that a thin film with small dynamic contact angle and driven by an external body force is unstable to the formation of fingers in the direction perpendicular to the main flow. The instability is largest in the capillary region near the contact line, where the force due to surface tension is comparable to the viscous and gravitational forces. The fastest growing wavelength is calculated in the limit of small-amplitude disturbances. These instabilities may be related to finger patterns observed in gravitational flows and spinning drops.

Patterning liquid flow on the microscopic scale

Microscopic fluidic devices, ranging from surgical endoscopes and microelectromechanical systems to the commercial ‘lab-on-a-chip’ (ref. 29), allow chemical analysis and synthesis on scales unimaginable a decade ago. These devices transport miniscule quantities of liquid along networked channels. Several techniques have been developed to control small-scale flow, including micromechanical and electrohydrodynamic pumping, electro-osmotic flow, electrowetting and thermocapillary pumping. Most of these schemes require micro-machining of interior channels and kilovolt sources to drive electrokinetic flow. Recent work has suggested the use of temperature instead of electric fields to derive droplet movement. Here we demonstrate a simple, alternative technique utilizing temperature gradients to direct microscopic flow on a selectively patterned surface (consisting of alternating stripes of bare and coated SiO2). The liquid is manipulated by simultaneously applying a shear stress at the air–liquid interface and a variable surface energy pattern at the liquid–solid interface. To further this technology, we provide a theoretical estimate of the smallest feature size attainable with this technique.

Thermocapillary actuation of droplets on chemically patterned surfaces by programmable microheater arrays

We have designed a microfluidic device for the actuation of liquid droplets or continuous streams on a solid surface by means of integrated microheater arrays. The microheaters provide control of the surface temperature distribution with high spatial resolution. These temperature gradients locally alter the surface tension along droplets and thin films thus propelling the liquid toward the colder regions. In combination with liquophilic and liquophobic chemical surface patterning, this device can be used as a logistic platform for the parallel and automated routing, mixing and reacting of a multitude of liquid samples, including alkanes, poly(ethylene glycol) and water.

Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations

We investigate the behavior of the slip length in Newtonian liquids subject to planar shear bounded by substrates with mixed boundary conditions. The upper wall, consisting of a homogenous surface of finite or vanishing slip, moves at a constant speed parallel to a lower stationary wall, whose surface is patterned with an array of stripes representing alternating regions of no shear and finite or no slip. Velocity fields and effective slip lengths are computed both from molecular dynamics (MD) simulations and solution of the Stokes equation for flow configurations either parallel or perpendicular to the stripes. Excellent agreement between the hydrodynamic and MD results is obtained when the normalized width of the slip regions, a/sigma greater than or approximately equal O (10) , where sigma is the (fluid) molecular diameter characterizing the Lennard-Jones interaction. In this regime, the effective slip length increases monotonically with a/sigma to a saturation value. For a/sigma less than or approximately O (10) and transverse flow configurations, the nonuniform interaction potential at the lower wall constitutes a rough surface whose molecular scale corrugations strongly reduce the effective slip length below the hydrodynamic results. The translational symmetry for longitudinal flow eliminates the influence of molecular scale roughness; however, the reduced molecular ordering above the wetting regions of finite slip for small values of a/sigma increases the value of the effective slip length far above the hydrodynamic predictions. The strong correlation between the effective slip length and the liquid structure factor representative of the first fluid layer near the patterned wall illustrates the influence of molecular ordering effects on slip in noninertial flows.

Microfluidic actuation by modulation of surface stresses

We demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or silicon substrate by combining chemical surface patterning with electronically addressable microheater arrays. Hydrophilic lanes designate the possible routes for liquid migration while activation of specific heater elements determine the trajectories. The induced temperature fields spatially modulate the liquid surface tension thereby providing electronic control over the direction, timing, and flow rate of continuous streams or discrete drops. Temperature maps can be programed to move, split, trap, and mix ultrasmall volumes without mechanically moving parts and with low operating voltages of 2–3 V. This method of fluidic actuation allows direct accessibility to liquid samples for handling and diagnostic purposes and provides an attractive platform for palm-sized and battery-powered analysis and synthesis.

Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions

The influence of surface roughness on the slip behaviour of a Newtonian liquid in steady planar shear is investigated using three different approaches, namely Stokes flow calculations, molecular dynamics (MD) simulations and a statistical mechanical model for the friction coefficient between a corrugated wall and the first liquid layer. These approaches are used to probe the behaviour of the slip length as a function of the slope parameter ka = 2πa/λ, where a and λ represent the amplitude and wavelength characterizing the periodic corrugation of the bounding surface. The molecular and continuum approaches both confirm a monotonic decay in the slip length with increasing ka but the rate of decay as well as the magnitude of the slip length obtained from the Stokes flow solutions exceed the MD predictions as the wall feature sizes approach the liquid molecular dimensions. In the limit of molecular-scale wall corrugation, a Green–Kubo analysis based on the fluctuation–dissipation theorem accurately reproduces the MD results for the behaviour of the slip length as a function of a. In combination, these three approaches provide a detailed picture of the influence of periodic roughness on the slip length which spans multiple length scales ranging from molecular to macroscopic dimensions.

Selective dip-coating of chemically micropatterned surfaces

We characterize the selective deposition of liquid microstructures on chemically heterogeneous surfaces by means of dip coating processes. The maximum deposited film thickness depends critically on the speed of withdrawal as well as the pattern size, geometry, and angular orientation. For vertically oriented hydrophilic strips, we derive a hydrodynamic scaling relation for the deposited film thickness which agrees very well with interferometric measurements of dip-coated liquid lines. Due to the lateral confinement of the liquid, our scaling relation differs considerably from the classic Landau–Levich formula for chemically homogeneous surfaces. Dip coating is a simple method for creating large area arrays of liquid microstructures for applications involving chemical analysis and synthesis, biochemical assays, or wet printing of liquid polymer or ink patterns.

Effect of contact angle hysteresis on thermocapillary droplet actuation

Open microfluidic devices based on actuation techniques such as electrowetting, dielectrophoresis, or thermocapillary stresses require controlled motion of small liquid droplets on the surface of glass or silicon substrates. In this article we explore the physical mechanisms affecting thermocapillary migration of droplets generated by surface temperature gradients on the supporting substrate. Using a combination of experiment and modeling, we investigate the behavior of the threshold force required for droplet mobilization and the speed after depinning as a function of the droplet size, the applied thermal gradient and the liquid material parameters. The experimental results are well described by a hydrodynamic model based on earlier work by Ford and Nadim. The model describes the steady motion of a two-dimensional droplet driven by thermocapillary stresses including contact angle hysteresis. The results of this study highlight the critical role of chemical or mechanical hysteresis and the need to reduce this retentive force for minimizing power requirements in microfluidic devices.

Morphology of liquid microstructures on chemically patterned surfaces

We study the equilibrium conformations of liquid microstructures on flat but chemically heterogeneous substrates using energy minimization computations. The surface patterns, which establish regions of different surface energy, induce deformations of the liquid–solid contact line. Depending on the geometry, these deformations either promote or impede capillary breakup and bulge formation. The contact angles of the liquid on the hydrophilic and hydrophobic regions, as well as the pattern geometry and volume of liquid deposited, strongly affect the equilibrium shapes. Moreover, due to the small scale of the liquid features, the presence of chemical or topological surface defects significantly influence the final liquid shapes. Preliminary experiments with arrays of parallel hydrophilic strips produce shapes resembling the simulated forms. These encouraging results provide a basis for the development of high resolution lithography by direct wet printing.