Dynamics of a climbing surfactant-laden film II: stability

The linear and nonlinear stability of a spreading film of constant flux and a drop of constant volume, discussed in [1], are examined here. A linear stability analysis (LSA) is carried out to investigate the stability to spanwise perturbations, by linearisation of the two-dimensional (2-D) evolution equations derived in [1] for the film thickness and surfactant concentration fields. The latter correspond to convective-diffusion equations for the surfactant, existing in the form of monomers (present at the free surface and in the bulk) and micelles (present in the bulk). The results of the LSA indicate that the thinning region, present upstream of the leading front in the constant flux case, and the leading ridge in the constant volume case, are unstable to spanwise perturbations. Numerical simulations of the 2-D system of equations demonstrate that the above-mentioned regions exhibit finger formation; the effect of selected system parameters on the fingering patterns is discussed.     

Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid-fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.     

Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility

The effect of bulk-soluble surfactants on the dynamics of a drop translating through a cylindrical tube under low-Reynolds-number conditions is investigated. Interfacial surfactant adsorption/desorption is modeled according to the Frumkin adsorption framework, and the bulk-insoluble surfactant limit is recovered as the rate of surfactant sorption becomes large compared to that of bulk diffusion. As the equilibrium surface coverage is increased, the mechanism by which drop mobility is reduced changes from uniform retardation at low surface coverage to the formation of a stagnant cap at high surface coverage. For large capillary numbers, the drop does not achieve a steady shape, and eventually it breaks up either through the formation of a penetrating viscous jet of suspending fluid, or by continuous elongation and pinch-off. Surfactants have a destabilizing effect on transient drop shapes by accelerating the formation and development of the penetrating viscous jet that leads to drop breakup. The critical conditions for drop breakup, as well as the mode of breakup, depend on the manner in which the strength of the flow (i.e., the capillary number) is increased.     

Dynamics of capillary flow of blood into a microfluidic channel

In this paper, a novel mathematical approach is devised to analyze the flow of blood from a droplet into a microcapillary channel. Special attention is devoted to estimate the effects of variable hydraulic resistance over different flow regimes, influence of suspended RBC particulates on the non-Newtonian flow characteristics and implications of a dynamically-evolving contact angle. Flow characteristics depicting advancement of the fluid within the microfluidic channel turn out to be typically non-linear, as per relative instantaneous strengths of the capillary forces and viscous resistances. It is found that the greater the 'pseudoplasticity' of the blood, the weaker the retarding shear forces. The driving forces, on the other hand, become stronger with time, on account of a reduction of contact angle with a decrease of blood flow velocity, although this strengthening is less prominent for blood samples with greater 'pseudoplasticity'. It is revealed that RBCs suspended in blood samples have a strong influence on the effective blood viscosity, and consequently, may drive the fluid significantly faster into the microchannel, especially when the characteristic length scales of the suspensions approach the hydraulic radius of the channel.     

Spreading, evaporation, and contact line dynamics of surfactant-laden microdrops

An optical technique based on the reflectivity measurements of a thin film was used to experimentally study the spreading, evaporation, contact line motion, and thin film characteristics of drops consisting of a water-surfactant (polyalkyleneoxide-modified heptamethyltrisiloxane, called superspreader) solution on a fused silica surface. On the basis of the experimental observations, we concluded that the surfactant adsorbs primarily at the solid-liquid and liquid-vapor interfaces near the contact line region. At equilibrium, the completely wetting corner meniscus was associated with a flat adsorbed film having a thickness of approximately 31 nm. The calculated Hamaker constant, A = -4.47 x 10(-)(20) J, shows that this thin film was stable under equilibrium conditions. During a subsequent evaporation/condensation phase-change process, the thin film of the surfactant solution was unstable, and it broke into microdrops having a finite contact angle. The thickness of the adsorbed film associated with the drops was lower than that of the equilibrium meniscus. The drop profiles were experimentally measured and analyzed during the phase-change process as the contact line advanced and receded. The apparent contact angle, the maximum concave curvature near the contact line region, and the convex curvature of the drop increased as the drop grew during condensation, whereas these quantities decreased during evaporation. The position of the maximum concave curvature of the drop moved toward the center of the drop during condensation, whereas it moved away from the center during evaporation. The contact line velocity was correlated to the observed experimental results and was compared with the results of the drops of a pure alcohol. The experimentally obtained thickness profiles, contact angle profiles, and curvature profiles of the drops explain how the surfactant adsorption affects the contact line motion. We found that there was an abrupt change in the velocity of the contact line when the adsorbed film of the surfactant solution was just hydrated or desiccated during the phase-change processes. This result shows the effect of vesicles and aggregates of the surfactant on the shape evolution of the drops. For these surfactant-laden water drops, we found that the apparent contact angle increased during condensation and decreased during evaporation. However, for the drop of a pure liquid (n-butanol and 2-propanol) the apparent contact angle remained constant at a constant velocity during condensation and evaporation. The contact line was pinned during the evaporation and spreading of the surfactant-laden water drops, but it was not pinned for a drop of a pure alcohol (self-similar shape evolution).     

Dynamics of attractive vesicles in shear flow

A nonequilibrium molecular dynamics (NEMD) method is employed to study the dynamics of two identical vesicles with attractive interactions immersed in shear flow. The dynamics behaviors of attractive vesicles depend on the attractive interactions and the shear rates simultaneously. There are four motion types for attractive vesicles in shear flow: a coupled-tumbling (CTB) motion, a coupled-trembling (CTR) motion, a collision/rotation mixture (CRM) motion and a separated-tank-treading (STT) motion, which are determined by the competition between the shear flow and the attractive interactions. Furthermore, the dynamics behavior of an individual vesicle shows three main motion types such as tumbling, trembling and tank-treading motions, and relies mainly on the shear rates. Meanwhile, comparisons with rigid vesicles for the dynamics behaviors are made, and the collision/rotation mixture (M) motion isn’t observed for rigid vesicles.     

Dynamics of adsorbed polymer chains subjected to flow: The dumbbell model

The dumbbell model of an adsorbed polymer segment is analyzed in order to investigate the response of such segments to a velocity gradient imposed at the solid/liquid interface. It is demonstrated that exact expressions for the time-dependent moments of the distribution function describing the conformation can be obtained. Both a dangling end and an attached loop can be represented and several bulk properties of a polymer film subjected to flow are evaluated.     

Dynamics of a stochastic model for continuous flow bioreactor with Contois growth rate

In the modelling of the continuous flow bioreactor, due to uncertainties in the environment the growth rate parameter is under perturbation of white noise, which results in a mathematical model governed by a set of stochastic differential equations. In this paper, assume the Contois growth rate is used and then we first show that the stochastic model has always a unique positive solution. Then long time behavior of the model is studied. Our study shows that both the washout and non-washout equilibria are stochastically stable. At the end, we carry out some numerical simulation, which supports our theoretical conclusion well. Also, by the quantities introduced in the last section, both residence time and intensity of the noise have significant effect on the performance of the reactor.     

Dynamics of relaxation of entangled polymers in shear flow

The application of shear flow to entangled polymer melts can strongly modify its rheological and physicochemical behaviors, giving rise to an acceleration of several chemical processes such as diffusion-controlled reactions. In the present work, we investigate the modification of conformational and diffusive properties of an entangled polymer in shear flow by numerical methods. The flow affects both the conformational and diffusive properties of the system, giving rise to a quasinematic ordering of the macromolecules which take prolate spheroid shape with the main axis aligned to the shear direction. The shear flow is found to accelerate the overall diffusion of the chains in all directions at times longer than the polymer relaxation time. The polymer chains display a quite peculiar displacement behavior in direction parallel to the flow. At the same conditions, the linear relation between the diffusion constant in direction perpendicular to the flow and the inverse of the relaxation time, usually adopted in equilibrium regimes, is shown to hold even in the presence of flow.     

Dynamics of admixture consumption from a gaseous flow in reaction with a solid reactant: An analytical solution to the problem

Dynamics of admixture consumption from gaseous flow during a reaction with a solid reactant is expressed in terms of a set of two partial differential equations. The analytical solution to the problem is found. The solution is illustrated by the plots of admixture distribution in the gas and absorbent.     

CFD evaluation of drop retraction methods for the measurement of interfacial tension of surfactant-laden drops

Drop retraction methods are popular means of measuring the interfacial tension between immiscible polymers. Experiments show that two different drop retraction methods, imbedded fiber retraction (IFR) and deformed drop retraction (DDR), give inconsistent results when a surfactant is present on the surface of the drop. These inconsistencies are deemed to be due to dilution of the surfactant and due to gradients in interfacial concentration of surfactant along the drop surface. This physical picture is quantified for the simple case of a Newtonian drop in a Newtonian matrix, with an insoluble, nondiffusive surfactant at the interface. The drop is deformed in computational fluid dynamics simulations by shearing the matrix, and then allowed to retract. Dilution and interfacial tension gradients effects are found to be especially large at the early stages of retraction, making IFR unsuitable for measuring the interfacial tension of surfactant-laden interfaces. The effects of surfactant dilution and gradients are found to persist even at late stages of retraction, causing the DDR method to underestimate the equilibrium interfacial tension significantly. The largest underestimates occur when the drop viscosity is lower than the matrix viscosity.     

Dynamics of liquid benzene: a cage analysis

Dynamics of single molecules in liquids, inspected in the picosecond time scale by means of spectroscopic measurements or molecular-dynamics (MD) simulations, reveals a complex behavior which can be addressed as due to local confinement (cage). This work is devoted to the analysis of cage structures in liquid benzene, obtained from MD simulations. According to a paradigm proposed for previous analysis of atomic and molecular liquids [see, for example, A. Polimeno, G. J. Moro, and J. H. Freed, J. Chem. Phys. 102, 8094 (1995)], the istantaneous cage structure is specified by the frame of axes which identifies the molecular configuration at the closest minimum on the potential-energy landscape. In addition, the modeling of the interaction potential between probe molecule and molecular environment, based on symmetry considerations, and its parametrization from the MD trajectories, allows the estimation of the structural parameters which quantify the strength of molecular confinement. Roto-translational dynamics of probe and related cage with respect to a laboratory frame, dynamics of the probe within the cage (vibrations, librations, re-orientational motions), and the restructuring processes of the cage itself are analyzed in terms of selected time self-correlation functions. A time-scale separation between the processes is established. Moreover, by exploiting the evidence of fast vibrational motions of the probe with respect to the cage center, an orientational effective potential is derived to describe the caging in the time scale longer than approximately 0.2 ps.     

Dynamics of heat transport in CNTs based Darcy saturated flow: Modeling through fractional simulations

Nanofluids have a vital role in many industries due to their novelty of heat transfer. Various mathematical techniques are required to simulate such problems. It can seem that traditional partial differential equations are incapable of analyzing and investigating the physical behavior of flow parameters affected by memory effects. This research communicates the implementation of the most interesting analytical method namely Prabhakar fractional derivative regarding the thermal flow of Casson fluid with single and multiwall carbon-nanotubes due to an inclined plate. The water and blood are considered as base particles. slip and Newtonian heating impacts for the thermal flow are also considered. The fractional modal of leading PDE's is attained by Prabhakar fractional derivative with various limiting cases. The generalized solution for the thermal and velocity field is simulated via the Laplace transformation method. The thermal expressions are modeled via Fourier expressions. Graphs are used to illustrate the influence and behaviour of key physical and fractional characteristics. The finding is that the temperature and velocity profiles of SWCNTs are more prominent than those of MWCNTs. Changing the fractional parameter values results in a greater rise in the velocity gradient for blood-based nanofluid than for water-based nanofluid.     

Polymer Dynamics in a Polymer-Solid Interphase: Molecular Dynamics Simulations of 1,4-Polybutadiene At a Graphite Surface

A chemically realistic model of 1,4-polybutadiene confined by graphite walls in a thin film geometry was studied by molecular dynamics simulations. The chemically realistic approach allows for a quantitative determination of a variety of experimentally accessible relaxation functions (e.g., dielectric, NMR, or neutron scattering responses). The simulations yield these experimental observables. Additionally, the simulations can be resolved as a function of distance to the solid interface on a much finer scale than experimentally possible, providing a detailed mechanistic picture of the segmental and large scale motions of polymers in the interfacial region between bulk polymer melts and solid walls. Extending the study of 1,4-polybutadiene on graphite to temperatures close to the glass transition temperature, we also address the question to what extent growing length scales associated with the glass transition influence the melt dynamics in the interphase. It was found that there is an interplay of this intrinsic slowing down with the adsorption/desorption kinetics of the chains close to the wall. It is argued that the monomer density changes near the wall can overcome the effect of rotational barriers only in a region of about 2 nm next to the wall.     

Dynamics of interacting Brownian particles: a diagrammatic formulation

We present a diagrammatic formulation of a theory for the time dependence of density fluctuations in equilibrium systems of interacting Brownian particles. To facilitate derivation of the diagrammatic expansion, we introduce a basis that consists of orthogonalized many-particle density fluctuations. We obtain an exact hierarchy of equations of motion for time-dependent correlations of orthogonalized density fluctuations. To simplify this hierarchy we neglect contributions to the vertices from higher-order cluster expansion terms. An iterative solution of the resulting equations can be represented by diagrams with three- and four-leg vertices. We analyze the structure of the diagrammatic series for the time-dependent density correlation function and obtain a diagrammatic interpretation of reducible and irreducible memory functions. The one-loop self-consistent approximation for the latter function coincides with mode-coupling approximation for Brownian systems that was derived previously using a projection operator approach.     

Dynamics of a paraffin crystal

Recently it has become possible to make a series of simulations on a supercomputer of the molecular motion of a pentacontane (C₅₀H₁₀₂) crystal containing close to 10000 atoms. Such a crystal is big enough to serve as a model of a macroscopic crystal. It can also serve as a model for polyethylene. The large volume of detailed information on the structure and motion permits a new level of understanding. Information on crystal appearance, pseudo-symmetric crystal structures, picosecond time-scale formation of conformational defects and the beginning of the melting process is presented.     

Dynamics of a laser-irradiated adatom

The dynamics of an adsorbed atom irradiated by an I.R. laser in resonance with a single pair of states of the vibrational adbond is studied. Using a non-perturbative treatment for the laser-adbond interaction, a master equation is derived, which governs the time evolution of the populations of the laser-dressed states of the adbond. The effect of resonant heating and laser-induced desorption, as an example of a possible laser-induced surface process, is discussed.     

Dynamics of a Spreading Nanodroplet: A Molecular Dynamic Simulation

The spreading of polymer nanodroplets upon a sudden change from partial to complete wetting on an ideally flat and structureless solid substrate has been studied by molecular dynamic simulations using a coarse‐grained bead‐spring model of flexible macromolecules. Tanner's law for the growth of the lateral droplet radius {R(t) ∝ t^0.1} is found to hold as long as the droplet does not disintegrate into individually moving chains. The data for the contact angle θ following from Tanner's law correspond to a dependence on time {θ(t) ∝ t^−0.3}. Our analysis of the mean square displacements of the polymer centers of mass reveals several dynamic regimes during the process of spreading. PACS numbers: 68.10.Gw, 05.70.Ln, 61.20.Ja, 8.45.Gd.

Molecular dynamics results for the average mean square displacement of all polymer chains plotted vs. time for a broad range of values for ε_wall.     

Dynamics of a polymer attached to a surface: Bead and spring model

The Smoluchowski formalism is used to solve the problem of a bead of frictional resistance β attached to a surface with a spring of force constant _k over which a linear shear field of strenght α flows. The power dissipation is given by βα²kT/_k. k and T have their usual meanings. The result is generalized to an n-bead polymer. It is found that the power dissipation of a Rouse model polymer attached to a surface at one end is twice that of an identical polymer flowing freely in solution. If the force constant _k arises from an entropy force, then, because of the effect of the surface on the number of polymer configurations, there is an additional factor of two. The same relationship is expected to also hold for the frequency-dependent power dissipation. It is argued that a net circulation exists in the beads above the surface and that the magnitude of the circulation is roughly comparable to that which exists in a polymer freely rotating in solution under a shear field of the same magnitude.     

Dynamics of analyte binding onto a metallophthalocyanine: NO/FePc

The gas-surface reaction dynamics of NO impinging on an iron(II) phthalocyanine (FePc) monolayer were investigated using King and Wells sticking measurements. The initial sticking probability was measured as a function of both incident molecular beam energy (0.09-0.4 eV) and surface temperature (100-300 K). NO adsorption onto FePc saturates at 3% of a monolayer for all incident beam energies and surface temperatures, suggesting that the final chemisorption site is confined to the Fe metal centers. At low surface temperature and low incident beam energy, the initial sticking probability is 40% and decreases linearly with increasing beam energy and surface temperature. The results are consistent with the NO molecule sticking onto the FePc molecules via physisorption to the aromatics followed by diffusion to the Fe metal center, or precursor-mediated chemisorption. The adsorption mechanism of NO onto FePc was confirmed by control studies of NO sticking onto metal-free H2Pc, inert Au111, and reactive Al111.