Brian G. Higgins

Linear stability of plane Poiseuille flow of two superposed fluids

Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.

Film flow on a rotating disk

Unsteady liquid film flow on a rotating disk is analyzed by asymptotic methods for low and high Reynolds numbers. The analysis elucidates how a film of uniform thickness thins when the disk is set in steady rotation. In the low Reynolds number analysis two time scales for the thinning film are identified. The long‐time‐scale analysis ignores the initial acceleration of the fluid layer and hence is singular at the onset of rotation. The singularity is removed by matching the long‐time‐scale expansion for the transient film thickness with a short‐time‐scale expansion that accounts for fluid acceleration during spinup. The leading order term in the long‐time‐scale solution for the transient film thickness is shown to be a lower bound for film thickness for all time. A short‐time analysis that accounts for boundary layer growth at the disk surface is also presented for arbitrary Reynolds number. The analysis becomes invalid either when the boundary layer has a thickness comparable to that of the thinning film...

Rayleigh–Taylor instability in thin viscous films

The behavior of a viscous fluid film bounded by a wall and a heavier overlying immiscible phase is examined in the limit of small Bond number. Evolution equations governing the behavior of the interface between the two fluids are derived for spatially periodic disturbances and studied numerically. The analysis shows that instability leads to a spectrum of steady‐state interfacial shapes characterized by film rupture and formation of pendant drops, such that gravity and interfacial forces are in balance. An energy stability analysis reveals that one drop per wavelength is the most energetically favorable. An extension of the analysis, based on the boundary integral method, is described for arbitrary Bond number and creeping flow conditions, aimed at identifying a Bond number below which stable pendant drops are possible. Simulations are shown for Bond numbers in the range 0.4≤B≤10 for fluids of equal viscosity. When the Bond number is relatively large, the interface takes the form of a circular front that ...

The effects of inertia and interfacial shear on film flow on a rotating disk

In this paper the issue is addressed of how a liquid film of uniform thickness thins on a rotating disk because of the action of centrifugal force. The Navier–Stokes equations in self‐similar form are solved numerically by a finite‐difference method. The effects of film inertia, disk acceleration protocols, and interfacial shear are studied. The numerical results show that inertia has a marked influence on the rate of thinning when the Reynolds number is large and that existing asymptotic theories are inadequate for predicting the transient film thickness. When the disk has a finite acceleration at start‐up, the effects of local inertia are important even at low Reynolds numbers and the thinning rate is reduced. When the overlying phase is a gas, interfacial shear enhances the rate of thinning at sufficiently long spinning times.

LANGMUIR-BLODGETT MULTILAYERS OF POLYMER-MEROCYANINE-DYE MIXTURES

Deposition studies of mixed monolayers of poly(methylmethacrylate) (PMMA) and merocyanine chromophore (M22) were carried out by the Langmuir-Blodgett technique. The equilibrium surface pressure vs. specific area of the monolayers at the air-water interface was measured for several mixtures. The specific area vs. film composition at a fixed surface pressure deviated from linear behavior. The deposition of the monolayer onto a glass substrate was Z type for mixtures with high PMMA content, while Y type was preferred for mixtures with high dye content. The former structure exhibited second harmonic generation and should be of considerable interest in exploring the non-linear optical effects in Langmuir-Blodgett films. When prepared under a class 100 modular laminar flow hood and observed with reflection microscopy, the films showed no evidence of aggregate formation, suggesting that the PMMA-M22 mixtures were miscible.

Second-harmonic generation in Langmuir-Blodgett films of hemicyanine-poly(octadecyl methacrylate) and hemicyanine-behenic acid

Abstract Second-harmonic generation (SHG) is used to probe the structure and order in monolayer and multilayer Langmuir-Blodgett (LB) films of highly polarizable dye molecules deposited on glass. Optical measurements on LB monolayers of hemicyanine-poly(octadecyl methacrylate) (PODMA) and hemicyanine-behenic acid mixtures in conjuction with data from compression isotherms show that the hemicyanine-PODMA system is immiscible and that the hemicyanine-behenic acid system is miscible. Incomplete Y-type LB multilayers of 54 mol.% hemicyanine in PODMA exhibited an erratic increase, which was less than linear, in the SHG with the number of layers deposited on the upstroke. Multilayer films of hemicyanine interleaved with behenic acid showed a slightly greater than quadratic increase in SHG with the number of hemocyanine layers deposited.

Future applications of ordered polymeric thin films

Abstract Polymeric ultrathin film systems need to be developed in the context of applications where their unique combinations of properties promise revolutionary improvements in performance or cost effectiveness. The applications examined include electron beam resists for microlithography and nanolithography, insulating films in semiconductor devices, non-linear optical elements and coatings for communications and computing, as well as highly permselective membranes in biotechnology. In this paper, we will review some of the most appealing suggestions and evaluate their current status. Improvements in film characterization and deposition based on Langmuir-Blodgett techniques are also suggested.

Marangoni flows during drying of colloidal films

In this study, we consider the drying of a thin film that contains a stable dispersion of colloidal particles so that a coating of these particles is formed after the liquid is driven off by evaporation. For sufficiently thin films, we show that evaporative cooling can drive a Marangoni flow that results in surface deformation of the drying film. A thin-film approximation is used to describe the velocity and temperature fields, and the particle transport equation with convective terms retained is used to describe the concentration field. A coupled finite difference/spectral element scheme is implemented numerically to solve the particle transport equation, where high accuracy is required to resolve sharp gradients within the film and to ensure particle conservation during drying. The model employed is capable of describing the evolution of film thickness and concentration field up to the time when maximum packing is nearly reached at some point in the domain. Three types of film structures are observed, all characterized by a final nonuniform thickness. In the first type, observed at low Peclet numbers, the maximum concentration is reached at the thinnest points in the film, which surround elevations with lower particle concentrations. This mode of instability suggests that dried coatings will have pronounced nonuniformities, resulting in the formation of craters or pinholes. In the second type, observed at high Peclet numbers, a closely packed skin of nonuniform thickness is formed, with low concentration fluid remaining beneath the elevations. In the final stages of drying one would expect capillary pressure to pull particles in the underlying fluid toward the skin, thus creating voids under a seemingly homogeneously applied coating. Finally, still at relatively large particle Peclet numbers and when the destabilizing Marangoni stresses are sufficiently strong, floating lumps of closely packed particles may form in the vicinity of film elevations.In this study, we consider the drying of a thin film that contains a stable dispersion of colloidal particles so that a coating of these particles is formed after the liquid is driven off by evaporation. For sufficiently thin films, we show that evaporative cooling can drive a Marangoni flow that results in surface deformation of the drying film. A thin-film approximation is used to describe the velocity and temperature fields, and the particle transport equation with convective terms retained is used to describe the concentration field. A coupled finite difference/spectral element scheme is implemented numerically to solve the particle transport equation, where high accuracy is required to resolve sharp gradients within the film and to ensure particle conservation during drying. The model employed is capable of describing the evolution of film thickness and concentration field up to the time when maximum packing is nearly reached at some point in the domain. Three types of film structures are observed, a...

Rupture of Thin Films: Nonlinear Stability Analysis

Abstract The instability and rupture of thin films due to a negative disjoining pressure is examined. A system of a thin film, bounded by a solid substrate and a second fluid phase semi-infinite in extent, is considered, and a nonlinear hydrodynamic stability analysis that takes into account the effects of the overlying fluid phase in a formal manner is presented. The analysis yields an evolution equation for the film thickness which reflects the effects of disjoining pressure and interfacial tension, as well as the dynamics of the two fluid phases. Limiting forms of the evolution equation are studied numerically to obtain qualitative features of the instability that cannot be captured by linear theory, and quantitative information about film rupture times.

Quadratically enhanced second harmonic generation in polymer-dye Langmuir-Blodgett films: A new bilayer architecture

Abstract A new double bilayer ABCC dippind sequence for the Langmuir-Blodgett deposition process has resulted in a one hundred-fold increase in second harmonic signal generation for ten ABCC sequences compared to one ABCC sequence. The AB bilayers are comprised of hemicyanine side chains on a polyether backbone. Two different polymer-dye compositions are used in each bilayer in order to have dipoles pointing in the same direction upon “Y” type deposition. Hydrophilic-hydrophilic interactions between polymer-dye bilayers are prevented by interleaving with a CC behenic acid bilayer, which also provides interlayer local field insulation.