Experimental verification of the formation mechanism for pillar arrays in nanofilms subject to large thermal gradients.

The free surface of molten nanofilms is known to undergo spontaneous formation of periodic protrusions when exposed to a large transverse thermal gradient. Early time measurements of the array pitch and growth rate in polymer melts confirm a formation process based on a long wavelength thermocapillary instability and not electrostatic attraction or acoustic phonon driven growth as previously believed. We find excellent agreement with theoretical predictions provided the nanofilm out-of-plane thermal conductivity is several times larger than bulk, an enhancement suggestive of polymer chain alignment.

Planar digital nanoliter dispensing system based on thermocapillary actuation.

We provide guidelines for the design and operation of a planar digital nanodispensing system based on thermocapillary actuation. Thin metallic microheaters embedded within a chemically patterned glass substrate are electronically activated to generate and control 2D surface temperature distributions which either arrest or trigger liquid flow and droplet formation on demand. This flow control is a consequence of the variation of a liquid's surface tension with temperature, which is used to draw liquid toward cooler regions of the supporting substrate. A liquid sample consisting of several microliters is placed on a flat rectangular supply cell defined by chemical patterning. Thermocapillary switches are then activated to extract a slender fluid filament from the cell and to divide the filament into an array of droplets whose position and volume are digitally controlled. Experimental results for the power required to extract a filament and to divide it into two or more droplets as a function of geometric and operating parameters are in excellent agreement with hydrodynamic simulations. The capability to dispense ultralow volumes onto a 2D substrate extends the functionality of microfluidic devices based on thermocapillary actuation previously shown effective in routing and mixing nanoliter liquid samples on glass or silicon substrates.

Formation of nanopillar arrays in ultrathin viscous films: the critical role of thermocapillary stresses.

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.

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.

Experimental study of entrainment and drainage flows in microscale soap films.

The thickness of freely suspended surfactant films during vertical withdrawal and drainage is investigated using laser reflectivity. The withdrawal process conducted at capillary numbers below 10(-3) generates initial film thicknesses in the micrometer range; subsequent thinning is predominantly impelled by capillary and not gravitational forces. Under these conditions, our results show that film thinning above and below the critical micelle concentration (cmc) is well approximated by a power law function in time whose exponents, which range from -0.9 to -1.8, are inconsistent with current descriptions of capillary-viscous drainage in inextensible films which predict exponents close to -0.5. Correlations between the experimental fitting parameters illustrate important differences in film behavior across the cmc. In addition, normalization of the drainage data yields a collapse to a single functional form over 3 decades in time for a wide range of initial withdrawal rates. We demonstrate that modification of the interface boundary condition in current models to account for Marangoni stresses through an effective slip parameter yields values of the exponents and other key parameters in excellent agreement with experiment. This modification also successfully describes the withdrawal thickness below the cmc.

Influence of boundary slip on the optimal excitations in thermocapillary driven spreading.

Thin liquid films driven to spread on homogeneous surfaces by thermocapillarity can undergo frontal breakup and parallel rivulet formation with well-defined wavelength. Previous modal analyses have relieved the well-known divergence in stress that occurs at a moving contact line by matching the front region to a precursor film. Because the linearized disturbance operator is non-normal, a generalized, nonmodal analysis is required to probe film stability at all times. The effect of the contact line model on nonmodal stability has not been previously investigated. This work examines the influence of boundary slip on thermocapillary driven spreading using a transient stability analysis, which recovers the conventional modal results in the long-time limit. In combination with earlier work on thermocapillary driven spreading, this study verifies that the dynamics and stability of this system are rather insensitive to the choice of contact line model and that the leading eigenvalue is physically determinant, thereby assuring results that agree with the eigenspectrum. Modal results for the flat precursor film model are reproduced with appropriate choice of slip coefficient and contact line slope.

Capacitive sensing of droplets for microfluidic devices based on thermocapillary actuation.

The design and performance of a miniaturized coplanar capacitive sensor is presented whose electrode arrays can also function as resistive microheaters for thermocapillary actuation of liquid films and droplets. Optimal compromise between large capacitive signal and high spatial resolution is obtained for electrode widths comparable to the liquid film thickness measured, in agreement with supporting numerical simulations which include mutual capacitance effects. An interdigitated, variable width design, allowing for wider central electrodes, increases the capacitive signal for liquid structures with non-uniform height profiles. The capacitive resolution and time response of the current design is approximately 0.03 pF and 10 ms, respectively, which makes possible a number of sensing functions for nanoliter droplets. These include detection of droplet position, size, composition or percentage water uptake for hygroscopic liquids. Its rapid response time allows measurements of the rate of mass loss in evaporating droplets.

Interfacial slip in entrained soap films containing associating hydrosoluble polymer.

Frankel's law predicts that the thickness of a Newtonian soap film entrained at small capillary number scales as Ca2/3 provided the bounding surfaces are rigid. Previous studies have shown that soap films containing low concentrations of high molecular weight (Mw) polymer can exhibit strong deviations from this scaling at low Ca, especially for associating surfactant-polymer solutions. We report results of extensive measurements by laser interferometry of the entrained film thickness versus Ca for the associating pair SDS/PEO over a large range in polymer molecular weight. Comparison of our experimental results to predictions of hydrodynamic models based on viscoelastic behavior shows poor agreement. Modification of the Frankel derivation by an interfacial slip condition yields much improved agreement. These experiments also show that the slip length increases as where zeta = 0.58 +/- 0.07. This correlation is suggestive of the Tolstoi-Larsen prediction that the slip length increases in proportion to the characteristic size of the fluid constituent despite its original derivation for liquid-solid interfaces.

Molecular origin and dynamic behavior of slip in sheared polymer films.

The behavior of the slip length in thin polymer films subject to planar shear is investigated using molecular dynamics simulations. At low shear rates, the slip length extracted from the velocity profiles correlates well with that computed from a Green-Kubo analysis. Beyond chain lengths of about N=10, the molecular weight dependence of the slip length is dominated strongly by the bulk viscosity. The dynamical response of the slip length with increasing shear rate is well captured by a power law up to a critical value where the momentum transfer between wall and fluid reaches its maximum.

Influence of attractive van der Waals interactions on the optimal excitations in thermocapillary-driven spreading.

Recent investigations of microfluidic flows have focused on manipulating the motion of very thin liquid films by modulating the surface tension through an applied streamwise temperature gradient. The extent to which the choice of contact line model affects the flow and stability of such thermocapillary-driven films is not completely understood. Regardless of the contact line model used, the linearized disturbance operator corresponding to the evolution of the film height is non-normal, and a generalized non-modal stability analysis is required. Surprisingly, early predictions of frontal instability that stemmed from conventional modal analysis of thermocapillary flow on a flat, infinite precursor film showed excellent agreement with experiment. Within the more rigorous framework provided by a generalized stability analysis, this work investigates the transient dynamics and amplification of optimal disturbances subject to a finite precursor film generated by attractive van der Waals forces. Convergence of the disturbance growth rates and perturbed shapes to the asymptotic solutions obtained by conventional linear stability analysis occurs early in the spreading process. In addition, the level of transient disturbance amplification is minimal. The equations governing thermocapillary-driven spreading exhibit a small degree of non-normality, which explains the source of agreement between modal theory and experiment. The more rigorous generalized stability analysis presented here, however, affords critical insight into the types of disturbances leading to maximum unstable growth and the exact influence of the contact line model used.

Growth and decay of localized disturbances on a surfactant-coated spreading film.

If the surface of a quiescent thin liquid film is suddenly coated by a patch of surface active material like a surfactant monolayer, the film is set in motion and begins spreading. An insoluble surfactant will rapidly attempt to coat the entire surface of the film thereby minimizing the liquid's surface tension. The shear stress that develops during the spreading process produces a maximum in surface velocity in the region where the moving film meets the quiescent layer. This region is characterized by a shock front with large interfacial curvature and a corresponding local buildup of surfactant which creates a spike in the concentration gradient. In this paper, we investigate the sensitivity of this region to infinitesimal disturbances. Accordingly, we introduce a measure of disturbance amplification and transient growth analogous to a kinetic energy that couples variations in film thickness to the surfactant concentration. These variables undergo significant amplification during the brief period in which they are convected past the downstream tip of the monolayer, where the variation in concentration gradient and surface curvature are largest. Once they migrate past this sensitive area, the perturbations weaken considerably and the system approaches a stable configuration. It appears that the localized disturbances of the type we consider here, cannot sustain asymptotic instability. Nonetheless, our study of the dynamics leading to the large transient growth clearly illustrates how the coupling of Marangoni and capillary forces work in unison to stabilize the spreading process against localized perturbations.

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures.

We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air-liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. [Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman (Materials Research Society, Boston, 1996), Vol. 464, p. 237; Phys. Fluids A 9, 3645 (1997); O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998]. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow [Phys. Fluids A 10, 1234 (1998); "Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances," submitted to Phys. Fluids]. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. (c) 1999 American Institute of Physics.