Lou Kondic

Predictability and granular materials

Abstract Granular materials present a number of challenges to predictability. The classical description of a dense granular material is based on Coulomb friction. For a static array of grains, the Coulomb friction forces are typically underdetermined. If we are to make useful statements about such arrays, we must develop new approaches, including the development of statistical descriptions. Granular materials also show large fluctuations in the local forces. These fluctuations are quite sensitive to small perturbations in the packing geometry of the grains. In the past, they have typically been ignored. However, recent experiments and models are beginning to shed new light on their characteristics. This article briefly reviews some of this new work, and in particular presents experimental results characterizing fluctuations and the role of friction in granular materials.

Self-Assembly versus Directed Assembly of Nanoparticles via Pulsed Laser Induced Dewetting of Patterned Metal Films

A nanoscale, synthetic perturbation was all that was required to nudge a natural, self-assembly process toward significantly higher order. Metallic thin film strips were transformed into nanoparticle arrays by nanosecond, liquid-phase dewetting. Arrays formed according to an evolving Rayleigh-Plateau instability, yet nanoparticle diameter and pitch were poorly controlled. However, by patterning a nanoscale sinusoid onto the original strip edge, a precise nanoparticle diameter and pitch emerged superseding the naturally evolving Rayleigh-Plateau instability.

Instabilities in Gravity Driven Flow of Thin Fluid Films

This paper presents theoretical, computational, and experimental aspects of the instability development in the flow of thin fluid films. The theoretical part involves basic fluid me- chanics and presents derivation of the thin film equation using lubrication approximation. A simplified version of this equation is then analyzed analytically using linear stability analysis, and also numerically. The results are then compared directly to experiments. The experimental part outlines the setup, as well as data acquisition and analysis. This immediate comparison to experiments is very useful for gaining better insight into the interpretation of various theoretical and computational results.

Pattern formation in the flow of thin films down an incline: Constant flux configuration

We present fully nonlinear time-dependent simulations of a thin liquid film flowing down an inclined plane. Within the lubrication approximation, and assuming complete wetting, we find that varying the inclination angle considerably modifies the shape of the emerging patterns: Finger-shaped patterns result for the flow down a vertical plane, while saw-tooth patterns develop for the flows down an inclined plane. However, in all of our simulations, the roots always move, indicating that the shape of the patterns is not necessarily related to the surface coverage, a technologically important feature of the flow. Furthermore, we find that triangular steady-state patterns may be produced for the flow down an incline, while the fingers typically grow in length for all explored times. We find quantitative agreement with reported experiments, and suggest new ones.

Particle Scale Dynamics in Granular Impact

We perform an experimental study of granular impact, where intruders strike 2D beds of photoelastic disks from above. High-speed video captures the intruder dynamics and the local granular force response, allowing investigation of grain-scale mechanisms in this process. We observe rich acoustic behavior at the leading edge of the intruder, strongly fluctuating in space and time, and we show that this acoustic activity controls the intruder deceleration, including large force fluctuations at short time scales. The average intruder dynamics match previous studies using empirical force laws, suggesting a new microscopic picture, where acoustic energy is carried away and dissipated.

On the breakup of patterned nanoscale copper rings into droplets via pulsed-laser-induced dewetting: competing liquid-phase instability and transport mechanisms.

Nanolithographically patterned copper rings were synthesized, and the self-assembly of the rings into ordered nanoparticle/nanodrop arrays was accomplished via nanosecond pulsed laser heating above the melt threshold. The resultant length scale was correlated to the transport and instability growths that occur during the liquid lifetime of the melted copper rings. For 13-nm-thick rings, a change in the nanoparticle spacing with the ring width is attributed to a transition from a Raleigh-Plateau instability to a thin film instability because of competition between the cumulative transport and instability timescales. To explore the competition between instability mechanisms further, we carried out experiments with 7-nm-thick rings. In agreement with the theoretical predictions, these rings break up in both the azimuthal and radial directions, confirming that a simple hydrodynamic model captures the main features of the processes leading to the breakup.

On the breakup of fluid films of finite and infinite extent

We study the dewetting process of thin fluid films that partially wet a solid surface. Using a long-wave (lubrication) approximation, we formulate a nonlinear partial differential equation governing the evolution of the film thickness, h. This equation includes the effects of capillarity, gravity, and an additional conjoining/disjoining pressure term to account for intermolecular forces. We perform standard linear stability analysis of an infinite flat film, and identify the corresponding stable, unstable, and metastable regions. Within this framework, we analyze the evolution of a semi-infinite film of length L in one direction. The numerical simulations show that for long and thin films, the dewetting fronts of the film generate a pearling process involving successive formation of ridges at the film ends and consecutive pinch-off behind these ridges. On the other hand, for shorter and thicker films, the evolution ends up by forming a single drop. The time evolution as well as the final drops pattern sho...

On the breakup of fluid rivulets

We study the stability of rivulets on horizontal substrates. The implemented model includes the effects of capillarity, fluid-solid interaction, and gravity if appropriate, within the framework of the lubrication approximation. We find that the results compare favorably with those in literature, in the regime where previous analyses are valid. By isolating the effect of van der Waals interactions for nanoscale rivulets, and of gravity for macrosize rivulets, we are able to analyze the influence of these forces on the stability. We discuss in detail the scaling of the emerging wavelengths (distance between drops formed after the breakup process) with the rivulet cross-sectional area. Perhaps surprisingly, we uncover close connection between this scaling and the one for the breakup of a free-space fluid jet (Rayleigh–Plateau instability). Finally, we consider rivulets of finite length and find that the finite size effects are considerably different from the ones obtained previously for semi-infinite fluid f...

Pattern formation in non-Newtonian Hele–Shaw flow

We study theoretically the Saffman–Taylor instability of an air bubble expanding into a non-Newtonian fluid in a Hele–Shaw cell, with the motivation of understanding suppression of tip-splitting and the formation of dendritic structures observed in the flow of complex fluids, such as polymeric liquids or liquid crystals. A standard visco-elastic flow model is simplified in the case of flow in a thin gap, and it is found that there is a distinguished limit where shear thinning and normal stress differences are apparent, but elastic response is negligible. This observation allows formulation of a generalized Darcy’s law, where the pressure satisfies a nonlinear elliptic boundary value problem. Numerical simulation shows that shear-thinning alone modifies considerably the pattern formation and can produce fingers whose tip-splitting is suppressed, in agreement with experimental results. These fingers grow in an oscillating fashion, shedding “side-branches” from their tips, closely resembling solidification patterns. A careful analysis of the parametric dependencies of the system provides an understanding of the conditions required to suppress tip-splitting, and an interpretation of experimental observations, such as emerging length-scales.

Competing Liquid Phase Instabilities during Pulsed Laser Induced Self-Assembly of Copper Rings into Ordered Nanoparticle Arrays on SiO2

Nanoscale copper rings of different radii, thicknesses, and widths were synthesized on silicon dioxide thin films and were subsequently liquefied via a nanosecond pulse laser treatment. During the nanoscale liquid lifetimes, the rings experience competing retraction dynamics and thin film and/or Rayleigh-Plateau types of instabilities, which lead to arrays of ordered nanodroplets. Surprisingly, the results are significantly different from those of similar experiments carried out on a Si surface. We use hydrodynamic simulations to elucidate how the different liquid/solid interactions control the different instability mechanisms in the present problem.