Shock Dynamics in Particle-Laden Thin Films

PRL 94(11) March 25, 2005 117803We present theory and experiments for thin film particle-laden flow on an incline. At higher particle concentration and inclination angle, a new phenomenon is observed in which a large particle-rich ridge forms at the contact line. We derive a lubrication theory for this system which is qualitatively compared to preliminary experimental data. The ridge formation arises from the creation of two shocks due to the differential transport rates of fluid and particles. This parallels recent findings of double shocks in thermal-gravity driven flow [A. L. Bertozzi et. al., PRL, 81, 5169 (1998), J. Sur et. al., PRL 90, 126105 (2003), A. M¨unch, PRL 91, 016105 (2003)]. However, here the emergence of the shocks arises from a new mechanism involving the settling rates of the species.NS

Dynamics of particle settling and resuspension in viscous liquids

We derive and study a dynamical model for suspensions of negatively buoyant particles on an incline. Our theoretical model includes the settling/sedimentation due to gravity as well as the resuspension of particles induced by shear-induced migration, leading to disaggregation of the dense sediment layer. Out of the three different regimes observed in the experiments, we focus on the so-called settled case, where the particles settle out of the flow, and two distinct fronts, liquid and particle, form. Using an approach relying on asymptotics, we systematically connect our dynamic model with the previously developed equilibrium theory for particle-laden flows. We show that the resulting transport equations for the liquid and the particles are of hyperbolic type, and study the dilute limit, for which we derive the analytic solution. We also carry out a systematic experimental study of the settled regime, focusing on the motion of the liquid and the particle fronts. Finally, we carry out numerical simulations of our transport equations. We show that the model predictions for small to moderate values of the particle volume fraction and the inclination angle of the solid substrate agree well with the experimental data

Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions

We review recent experiments on dewetting thin films of evaporating colloidal nanoparticle suspensions (nanofluids) and discuss several theoretical approaches to describe the ongoing processes including coupled transport and phase changes. These approaches range from microscopic discrete stochastic theories to mesoscopic continuous deterministic descriptions. In particular, we describe (i) a microscopic kinetic Monte Carlo model, (ii) a dynamical density functional theory and (iii) a hydrodynamic thin film model. Models (i) and (ii) are employed to discuss the formation of polygonal networks, spinodal and branched structures resulting from the dewetting of an ultrathin ‘postcursor film’ that remains behind a mesoscopic dewetting front. We highlight, in particular, the presence of a transverse instability in the evaporative dewetting front, which results in highly branched fingering structures. The subtle interplay of decomposition in the film and contact line motion is discussed. Finally, we discuss a simple thin film model (iii) of the hydrodynamics on the mesoscale. We employ coupled evolution equations for the film thickness profile and mean particle concentration. The model is used to discuss the self-pinning and depinning of a contact line related to the ‘coffee-stain’ effect. In the course of the review we discuss the advantages and limitations of the different theories, as well as possible future developments and extensions

Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film

We employ a recently proposed model [Murisic et al., "Dynamics of particle settling and resuspension in viscous liquids," J. Fluid. Mech. 717, 203-231 (2013)] to study a finite-volume, particle-laden thin film flowing under gravity on an incline. For negatively buoyant particles with concentration above a critical value and buoyant particles, the particles accumulate at the front of the flow forming a particle-rich ridge, whose similarity solution is of the rarefaction-singular shock type. We investigate the structure in detail and find that the particle/fluid front advances linearly to the leading order with time to the one-third power as predicted by the Huppert solution [H. E. Huppert, "Flow and instability of a viscous current down a slope," Nature 300, 427-419 (1982)] for clear fluid (i.e., in the absence of particles). We also explore a deviation from this law when the particle concentration is high. Several experiments are carried out with both buoyant and negatively buoyant particles whose results qualitatively agree with the theoretics

Models for the two-phase flow of concentrated suspensions

A new two-phase model for concentrated suspensions is derived that incorporates a constitutive law combining the rheology for non-Brownian suspension and granular flow. The resulting model exhibits a yield-stress behavior for the solid phase depending on the collision pressure. This property is investigated for the simple geometry of plane Poiseuille flow, where an unyielded or jammed zone of finite width arises in the center of the channel. For the steady states of this problem, the governing equations are reduced to a boundary value problem for a system of ordinary differential equations and the conditions for existence of solutions with jammed regions are investigated using phase-space methods. For the general time-dependent case a new drift-flux model is derived using matched asymptotic expansions that takes into account the boundary layers at the walls and the interface between the yielded and unyielded region. The drift-flux model is used to numerically study the dynamic behavior of the suspension flow including the appearance and evolution of an unyielded or jammed region

Long-wave Dynamics of Single- and Two-layer Flows

Thin-film flows are central to a number of industrial, biomedical and daily-life applications, which include coating flow technology, enhanced oil recovery, microfluidics, and surfactant replacement therapy. Though these systems have received a lot of attention in a variety of settings, the understanding of the dominant physics governing the flows is not completely thorough; this is especially true in cases where the free surface of the film or, in two-layer flows, the fluid-fluid interface is susceptible to instabilities leading to the break-up of the film and the formation of fingering patterns. The elucidation of the underlying mechanisms behind the onset of these instabilities is of utmost importance to several industrial processes. The work in this thesis focusses on modelling the dynamics of thin-film flows in the presence of complexities; the latter arise from the presence of surface-active chemicals and spatial confinement. The lubrication approximation, which is valid in the limit of small film aspect ratios, is used to simplify the governing equations; this facilitates the derivation of an evolution equation for the interfacial position. This methodology is employed extensively in the present thesis to examine co- and counter-current two-layer flows in a closed, rectangular channel and the dynamics of a thin film laden with surfactant, driven to climb up an inclined substrate. In the two-fluid case, the dynamics of the flow are described by a single, two-dimensional, fourth-order nonlinear partial differential equation. Analysis of the one-dimensional flow demonstrate the existence of travelling-wave solutions which take the form of Lax shocks, undercompressive shocks, and rarefaction waves. In unstably-stratified cases, a Rayleigh-Taylor mechanism spawns the formation of large-amplitude capillary waves. A wide range of parameters is studied, which include the density and viscosity ratios of the two fluids, the flow configuration (whether co- or counter-current), the heights of the films at the channel ends and the channel inclination. The stability of these structures to perturbations in the spanwise direction, is also examined through a linear stability analysis and transient, two-dimensional numerical simulations. These analyses demonstrate successfully that some of the structures observed in the one-dimensional flow are unstable to fingering phenomena. In the case of the climbing film, two configurations are examined, namely, constant flux and constant volume whereby the evolution equation for the interface is coupled to convective-diffusive equations for the concentration of surfactant, present in the form of monomers and micelles. The former are allowed to exist at the gas-liquid and liquid-solid interfaces, and in the bulk; the latter can only be present in the bulk. For the constant flux case, the flow is simulated by a continuously-fed uncontaminated fluid and surfactant at the flow origin allowed to spread on a solid substrate which has been prewetted by a thin, surfactant-free precursor layer. The constant volume configuration simulates the deposition of a finite drop, laden with surfactant, spreading on a thin, uncontaminated film. In the absence of spanwise disturbances, the one-dimensional solutions demonstrate how the climbing rate and the structural deformation of the film are influenced by gravity, and physico-chemical parameters such as surfactant concentration (whether above or below the critical micelle concentration), and rates of adsorption of monomers at the two interfaces. The stability of the flow is examined through linear theory and transient solutions of the full, nonlinear, two-dimensional system of equations revealing the growth of spanwise perturbations into full-length fingers. A brief introduction to the experimental design of an apparatus, aimed at validating channel flow results, is also described. The objective of the experiment was to investigate the physical features associated with the counter-current, pressure-driven flow of a gas-liquid system. Preliminary experimental results revealed that upon perturbing the flow, an initially uniform liquid film becomes unstable, resulting in the formation of fingers which elongated downstream as time progressed. Finally, we conclude with recommendations for future work, representing natural extensions to the theoretical work described in the present thesis

Reduced model for particle laden flow

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2004.Includes bibliographical references (p. 133-138).The flow of thin liquid films on solid surfaces is a significant phenomenon in nature and in industrial processes where uniformity and completeness of wetting are paramount in importance. It is well known that when a clear viscous fluid flows down an inclined surface under gravity, after some time, the initially straight contact line becomes unstable with respect to transverse perturbations. Clear fluid is easier to use in experiments, but industrial processes usually involve particulates in the form of either suspensions or dry granular flows. In this work, we study the flow of a thin film down an inclined plane. The particle-fluid mixture is modeled as a single fluid with effective density and viscosity, depending on the concentration of the particles. Since the flow is slow and the fluid layer is very thin, inertial effects are ignored and a lubrication approximation is applied to simplify the analysis. It is assumed that there is no variation in the transverse direction before the onset of instability, and the fluid properties and velocity are depth averaged to remove the height-dependence. The settling velocity of the particles is hindered by the presence of neighboring particles; this phenomenon is captured by the hindered velocity function that decreases with increasing concentration. The normal component of the settling velocity is neglected in this work and the resulting model is a system of two equations accounting for the film thickness and particle concentration changes as the mixture flows down the plane. Numerical simulations are performed and it is found that the mixtures with higher concentration flow more slowly. Compared to the clear viscous fluid, particle laden flow results in a bump that is much bigger and the size of the bump(cont.) bump increases with concentration. We also observe that the front edge of the bump travels faster than the trailing edge and the bump width increases. Numerical simulations reveal that an intermediate plateau structure due to the presence of particles is formed behind the smaller bump due to surface tension. This intermediate state depends on the inclination angle and the initial concentration. When the higher order terms in our derived model are dropped, we discover that the resulting reduced model is still able to capture the bulk characteristics of the flow. The reduced model is a 2X2 system of conservation laws, in which the solutions can be obtained through classical shock theory analysis. It is found that our system involves a 1-shock at the trailing edge connected by an intermediate state to a 2-shock at the leading edge. The intermediate state as well as the shock speeds can be solved by shock theory analysis, and their values are found to agree very well with the simulations.by Junjie Zhou.S.M

ELECTROSTATIC FOCUSING AND IMPACT CONSOLIDATION OF AEROSOL PARTICLES

ELECTROSTATIC FOCUSING AND IMPACT CONSOLIDATION OF AEROSOL PARTICLE