Newtonian Thin Films

Thin films provide a rich setup that is of interest from multiple points of view. From application side, these thin films and their instabilities are of relevance to a number of fields that rangefrom glass making to semiconductor and polymer applications, solar cells, to mention just a few fields of applications. From modeling side, thin films are demanding due to the presence of multiple spatial and temporal scales and due to the need to incorporate multi physics that is often of relevance in particular in the setups involving spreading and instabilities of thin films on substrates.

Recent group activities on the topic of Newtonian thin films have focused on modeling and simulations of metal films of nanoscale thickness exposed to laser radiation, in collaboration with the experimental group at U. Tennessee and Oak Ridge National Laboratory. Metal films are relevant to a number of technological fields with applications that include plasmonics, magnetic nanoparticles, control surface optical properties, catalysts for nanowire growth and many others. In many of these fields ordered arrays of nanoparticles are needed. While in liquid phase, the film instabilities lead to such arrays via self- or directed- assembly, and we are interested in the basic mechanisms that are relevant to the instabilities.

At NJIT, we have carried extensive simulations of thin metal films within the long-wave model that reduces the problem to solving a nonlinear 4th order evolution equation of diffusion type, as well as by directly solving Navier-Stokes equations using Volume-of-Fluid method. A number of new and interesting results has been obtained, including much better understanding of the connection between film instability and its geometry, of the influence of fluid/solid interaction forces, heat flow through the film and the substrate, to name just a few aspects.

Earlier works on thin films include a variety of configurations and setups including considerations of stochastic effects, flows down an incline, hanging and evaporating films, among others. Some of the considered configurations were also explored in research projects including undergraduate students in the Capstone Laboratory [link to the capstone page]. The relevant recent publications can be found below, and older works are listed at the publication list or here.

We acknowledge past and current support by NSF and Fulbright Foundation.

Recent Publications

T-S, Lin; Dijksman,J. A.; and Kondic,L., Thin liquid films in a funnel, Journal of Fluid Mechanics, 924, A26:1-A26:22, (2021)

We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. While the flow in a funnel may be related to a number of other flow configurations as limiting cases, understanding its stability is complicated due to the presence of additional azimuthal curvature, as well as due to convergent flow effects imposed by the geometry. The convergent nature of the flow leads to thickening of the film, therefore influencing its stability properties. In this work, we analyse these stability properties by combining physical experiments, asymptotic modelling, self-similar type of analysis and numerical simulations. We show that an appropriate long-wave-based model, supported by the input from experiments, simulations and linear stability analysis that originates from the flow down an incline plane, provides a basic insight allowing an understanding of the development of contact line instability and emerging length scales.

L. Hauer, W. S. Y Wong, V. Donadei, K.I. Hegner, L. Kondic, and D. Vollmer, How Frost Forms and Grows on Lubricated Micro- and Nanostructured Surfaces, ACS Nano, 15, 4658-4668, (2021)

Frost is ubiquitously observed in nature whenever warmer and more humid air encounters colder than melting point surfaces (e.g., morning dew frosting). However, frost formation is problematic as it damages infrastructure, roads, crops, and the efficient operation of industrial equipment (i.e., heat exchangers, cooling fins). While lubricant-infused surfaces offer promising antifrosting properties, underlying mechanisms of frost formation and its consequential effect on frost-to-surface dynamics remain elusive. Here, we monitor the dynamics of condensation frosting on micro- and hierarchically structured surfaces (the latter combines micro- with nanofeatures) infused with lubricant, temporally and spatially resolved using laser scanning confocal microscopy. The growth dynamics of water droplets differs for micro- and hierarchically structured surfaces, by hindered drop coalescence on the hierarchical ones. However, the growth and propagation of frost dendrites follow the same scaling on both surface types. Frost propagation is accompanied by a reorganization of the lubricant thin film. We numerically quantify the experimentally observed flow profile using an asymptotic long-wave model. Our results reveal that lubricant reorganization is governed by two distinct driving mechanisms, namely: (1) frost propagation speed and (2) frost dendrite morphology. These in-depth insights into the coupling between lubricant flow and frost formation/propagation enable an improved control over frosting by adjusting the design and features of the surface.

R. H. Allaire, L. Kondic, L. J. Cummmings, P. Rack, and M. Fuentes-Cabrera, The Role of Phase Separation on Rayleigh-Plateau Type Instabilities in Alloys, J. Phys. Chem. C, 125, , (2021)

Classical molecular dynamics(MD) simulation sare used to investigate the role of phase separation (PS) on the Rayleigh Plateau (RP) instability. Ni−Ag bulk structures are created at temperatures (2000K and 1400K) that generate different PS lengthscales, relative to the RP instability length scale. Rectanguloids are then cut from the bulk structures and patterned with a perturbation of certain amplitude and wavelength. It is found that the patterned rectanguloids break up into nanoparticles in a manner consistent with classical RP theory. Thus, we demonstrate that the phase separation length scale of an immiscible alloy can be exploited to direct the assembly of functional bimetallic alloys.

R. H. Allaire, L. J. Cummings, and L. Kondic, On efficient asymptotic modelling of thin films on thermally conductive substrates, Journal of Fluid Mechanics, 915, A133, (2021)

We consider a free-surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a set-up where the heat absorption depends on the local film thickness. Our focus is on modelling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film’s material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of-plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a set-up commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered set-up the Marangoni (thermocapillary) effect turns out to be insignificant.

R. H. Allaire, A. Dhakane, R. Emery, P. Ganesh, P. D. Rack, L. Kondic, L. Cummings, and M. Fuentes-Cabrera, Surface, Interface, and Temperature Effects on the Phase Separation and Nanoparticle Self Assembly of Bi-Metallic Ni0.5Ag0.5: A Molecular Dynamics Study, Nanomaterials, 9, 1040, (2019)

Classical molecular dynamics (MD) simulations were used to investigate how free surfaces, as well as supporting substrates, affect phase separation in a NiAg alloy. Bulk samples, droplets, and droplets deposited on a graphene substrate were investigated at temperatures that spanned regions of interest in the bulk NiAg phase diagram, i.e., miscible and immiscible liquid, liquid-crystal, and crystal-crystal regions. Using MD simulations to cool down a bulk sample from 3000 K to 800 K, it was found that phase separation below 2400 K takes place in agreement with the phase diagram. When free surface effects were introduced, phase separation was accompanied by a core-shell transformation: spherical droplets created from the bulk samples became core-shell nanoparticles with a shell made mostly of Ag atoms and a core made of Ni atoms. When such droplets were deposited on a graphene substrate, the phase separation was accompanied by Ni layering at the graphene interface and Ag at the vacuum interface. Thus, it should be possible to create NiAg core-shell and layer-like nanostructures by quenching liquid NiAg samples on tailored substrates. Furthermore, interesting bimetallic nanoparticle morphologies might be tuned via control of the surface and interface energies and chemical instabilities of the system.

W. Batson, L. J. Cummings, D. Shirokoff, and L. Kondic, Oscillatory thermocapillary instability of a film heated by a thick substrate, Journal of Fluid Mechanics, 872, 928-962, (2019)

In this work we consider a new class of oscillatory instabilities that pertain to thermocapillary destabilization of a liquid film heated by a solid substrate. We assume the substrate thickness and substrate–film thermal conductivity ratio are large so that the effect of substrate thermal diffusion is retained at leading order in the long-wave approximation. As a result, the system dynamics is described by a nonlinear partial differential equation for the film thickness that is non-locally coupled to the full substrate heat equation. Perturbing about a steady quiescent state, we find that its stability is described by a non-self-adjoint eigenvalue problem. We show that, under appropriate model parameters, the linearized eigenvalue problem admits complex eigenvalues that physically correspond to oscillatory (in time) instabilities of the thin-film height. As the principal results of our work, we provide a complete picture of the susceptibility to oscillatory instabilities for different model parameters. Using this description, we conclude that oscillatory instabilities are more relevant experimentally for films heated by insulating substrates. Furthermore, we show that oscillatory instability where the fastest-growing (most unstable) wavenumber is complex, arises only for systems with sufficiently large substrate thicknesses. Finally, we discuss adaptation of our model to a practical setting and make predictions of conditions at which the reported instabilities can be observed.

I. Seric, S. Afkhami, and L. Kondic, Direct numerical simulation of variable surface tension flows using a Volume-of-Fluid method, Journal of Computational Physics, 352, 615-636, (2018)

We develop a general methodology for the inclusion of a variable surface tension coefficient into a Volume-of-Fluid based Navier-Stokes solver. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation is applicable to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. We demonstrate the applicability of our method to the thermocapillary migration of bubbles and the coalescence of drops characterized by a different surface tension coefficient.

F. Font, S. Afkhami, and L. Kondic, Substrate melting during laser heating of nanoscale metal films, International Journal of Heat and Mass Transfer, 113, 237-245, (2017)

Abstract We investigate heat transfer mechanisms relevant to metal films of nanoscale thickness deposited on a silicon (Si) substrate coated by a silicon oxide (SiO2) layer and exposed to laser irradiation. Such a setup is commonly used in the experiments exploring self and directed assembly of metal films that melt when irradiated by laser and then evolve on time scale measured in nanoseconds. We show that in a common experimental setting, not only the metal but also the SiO2 layer may melt. Our study of the effect of the laser parameters, including energy density and pulse duration, shows that melting of the substrate occurs on spatial and temporal scales that are of experimental relevance. Furthermore, we discuss how the thicknesses of metal and of the substrate itself influence the maximum depth and liquid lifetime of the melted SiO2 layer. In particular, we find that there is a minimum thickness of SiO2 layer for which this layer melts and furthermore, the melting occurs only for metal films of thickness in a specified range. In the experiments, substrate melting is of practical importance since it may significantly modify the evolution of the deposited nanoscale metal films or other geometries on nanoscale.

K. Mahady, S. Afkhami, and L. Kondic, On the influence of initial geometry on the evolution of fluid filaments, Physics of Fluids, 27, 092104, (2015)

In this work, the influence of the initial geometry on the evolution of a fluid filament deposited on a substrate is studied, with a particular focus on the thin fluid strips of nano-scale thickness. Based on the analogy to the classical Rayleigh-Plateau (R-P) instability of a free-standing fluid jet, an estimate of the minimal distance between the final states (sessile droplets) can be obtained. However, this numerical study shows that while the prediction based on the R-P instability mechanism is highly accurate for an initial perturbation of a sinusoidal shape, it does not hold for a rectangular waveform perturbation. The numerical results are obtained by directly solving fully three-dimensional Navier-Stokes equations, based on a Volume of Fluid interface tracking method. The results show that (i) rectangular-wave perturbations can lead to the formation of patterns characterized by spatial scales that are much smaller than what is expected based on the R-P instability mechanism; (ii) the nonlinear stages of the evolution and end states are not simply related, with a given end state resulting from possibly very different types of evolution; and (iii) a variety of end state shapes may result from a simple initial geometry, including one- and two-dimensional arrays of droplets, a filament with side droplets, and a one-dimensional array of droplets with side filaments. Some features of the numerical results are related to the recent experimental study by Roberts et al. ["Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms," ACS Appl. Mater. Interfaces 5, 4450 (2013)].

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L. Kondic, N. Dong, Y. Wu, J.D. Fowlkes, and P.D. Rack, Instabilities of nanoscale patterned metal films, The European Physical Journal Special Topics, 224, 369-378, (2015)

We consider the evolution and related instabilities of thin metal films liquefied by laser pulses. The films are patterned by largescale perturbations and we discuss how these perturbations influence the dynamics. In the experiments, we find that the considered thin films dewet, leading to the formation of primary and secondary drops, with the locations of the primary ones coinciding with the original perturbations. Based on the results of the fully nonlinear time-dependent simulations, we discuss the details of the evolution leading to these patterns. Furthermore, in both experiments and simulations, we discuss the influence of the shape of the initial perturbations on the properties of the final patterns.

S. Afkhami and L. Kondic, On the dewetting of liquefied metal nanostructures, Journal of Engineering Mathematics, 94, 5-18, (2015)

Direct numerical simulations of liquefied metal nanostructures dewetting a substrate are carried out. Full three-dimensional Navier–Stokes equations are solved and a volume-of-fluid method is used for tracking and locating the interface. Substratewettability is varied to study the influence of the solid–liquid interaction. The effects of initial geometry on the retraction dynamics is numerically investigated. It is shown that the dewetting velocity increases with increases in the contact angle and that the retraction dynamics is governed by an elaborate interplay of initial geometry, inertial and capillary forces, and the dewetting phenomena. Numerical results are presented for the dewetting of nanoscale Cu and Au liquefied structures on a substrate.

S. Afkhami and L. Kondic, Numerical simulation of ejected molten metal nanoparticles liquified by laser irradiation: Interplay of geometry and dewetting, Physical Review Letters, 111, 034501, (2013)

Metallic nanoparticles, liquified by fast laser irradiation, go through a rapid change of shape attempting to minimize their surface energy. The resulting nanodrops may be ejected from the substrate when the mechanisms leading to dewetting are sufficiently strong, as in the experiments involving gold nanoparticles [Habenicht et al., Science 309, 2043 (2005)]. We use a direct continuum-level approach to accurately model the process of liquid nanodrop formation and the subsequent ejection from the substrate. Our computations show a significant role of inertial effects and an elaborate interplay of initial geometry and wetting properties: e.g., we can control the direction of ejection by prescribing appropriate initial shape and/or wetting properties. The basic insight regarding ejection itself can be reached by considering a simple effective model based on an energy balance. We validate our computations by comparing directly with the experiments specified above involving the length scales measured in hundreds of nanometers and with molecular dynamics simulations on much shorter scales measured in tens of atomic diameters, as by M. Fuentes-Cabrera et al. [Phys. Rev. E 83, 041603 (2011)]. The quantitative agreement, in addition to illustrating how to control particle ejection, shows utility of continuum-based simulation in describing dynamics on nanoscale quantitatively, even in a complex setting as considered here.

A.G. González, J.A. Diez, Y. Wu, J.D. Fowlkes, P.D. Rack, and L. Kondic, Instability of Liquid Cu Films on a SiO2 Substrate, Langmuir, 29, 9378-9387, (2013)

We study the instability of nanometric Cu thin films on SiO2 substrates. The metal is melted by means of laser pulses for some tens of nanoseconds, and during the liquid lifetime, the free surface destabilizes, leading to the formation of holes at first and then in later stages of the instability to metal drops on the substrate. By analyzing the Fourier transforms of the SEM (scanning electron microscope) images obtained at different stages of the metal film evolution, we determine the emerging length scales at relevant stages of the instability development. The results are then discussed within the framework of a long-wave model. We find that the results may differ whether early or final stages of the instability are considered. On the basis of the interpretation of the experimental results, we discuss the influence of the parameters describing the interaction of the liquid metal with the solid substrate. By considering both the dependence of dominant length scales on the film thickness and the measured contact angle, we isolate a model which predicts well the trends found in the experimental data.

A.G. González, J.A. Diez, and L. Kondic, Stability of a liquid ring on a substrate, Journal of Fluid Mechanics, 718, 246-279, (2013)

We study the stability of a viscous incompressible fluid ring on a partially wetting substrate within the framework of long-wave theory. We discuss the conditions under which a static equilibrium of the ring is possible in the presence of contact angle hysteresis. A linear stability analysis (LSA) of this equilibrium solution is carried out by using a slip model to account for the contact line divergence. The LSA provides specific predictions regarding the evolution of unstable modes. In order to describe the evolution of the ring for longer times, a quasi-static approximation is implemented. This approach assumes a quasi-static evolution and takes into account the concomitant variation of the instantaneous growth rates of the modes responsible for either collapse of the ring into a single central drop or breakup into a number of droplets along the ring periphery. We compare the results of the LSA and the quasi-static model approach with those obtained from nonlinear numerical simulations using a complementary disjoining pressure model. We find remarkably good agreement between the predictions of the two models regarding the expected number of drops forming during the breakup process.

T.-S. Lin, L. Kondic, and A. Filippov, Thin films flowing down inverted substrates: Three-dimensional flow, Physics of Fluids, 24, 022105, (2012)

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three-dimensional setting. In the previous work [T.-S. Lin and L. Kondic, Phys. Fluids 22, 052105 (2010)], we considered two-dimensional flow, finding formation of surface waves whose properties within the implemented longwave model depend on a single parameter, D = (3Ca)1/3 cot α , where Ca is the capillary number and α is the inclination angle. In the present work we consider fully 3D setting and discuss the influence of the additional dimension on stability properties of the flow. In particular, we concentrate on the coupling between the surface instabilities and the transverse (fingering) instabilities of the film front. We furthermore consider these instabilities in the setting where fluid viscosity varies in the transverse direction. It is found that the flow pattern strongly depends on the inclination angle and the viscosity gradient.

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J.A. Diez, A.G. González, and L. Kondic, Instability of a transverse liquid rivulet on an inclined plane, Physics of Fluids, 24, 032104, (2012)

This work concentrates on the stability of a viscous liquid rivulet positioned across an inclined plane under partial wetting conditions. The study is performed within the framework of lubrication approximation by employing a slip model. Both normal and parallel components of gravity are considered.We find the stability regions for given area of the cross section of the rivulet, A, plane inclination angle, α, and static contact angle, θ0, characterizing the wettability of the substrate. For αs smaller than some critical angle, α*, a static solution exists. This solution is characterized by rear/front contact angles given by θ0 ± δ. The linear stability analysis of this solution is performed using an efficient pseudo-spectral Chebyshev method.We analyze the effects of A, θ0, and α on the predictions of the model, such as the dominant wavelength, the maximum growth rate, and the behavior of the most unstable perturbation mode. To verify them, we also carry out experiments with silicone oils spreading on a coated glass substrate for several different fluid volumes and inclination angles. We find very good agreement between the wavelength of maximum growth rate given by the theory and the average distance between the drops after rivulet breakup. An analysis of finite size effects shows that the inclusion of normal gravity effects leads to a better agreement between theoretical and experimental results.