Flow-Induced Concentration Nonuniformity and Shear Banding in Entangled Polymer Solutions.

Recent models have predicted entangled polymer solutions could shear band due to unstable flow-induced demixing. This work provides the first experimental probe of the in situ concentration profile of entangled polymer solutions under shear. At shear rates above a critical value, we show that the concentration and velocity profiles can develop bands, in quantitative agreement with steady-state model predictions. These findings highlight the critical importance of flow-concentration coupling in entangled polymer solutions.

Universal Gas Adsorption Mechanism for Flat Nanobubble Morphologies.

The adsorption of gas molecules at the substrate beneath interfacial nanobubbles modifies the energy of the solid-gas interface, and therefore affects their morphology. In this work, we describe a simple thermodynamic model that captures the influence of gas adsorption and gives flat bubble shapes with reduced gas-side contact angles relative to the zero-adsorption case, in agreement with experimental studies. We show that this effect is general to both hydrophilic and hydrophobic substrates and has a stabilizing influence that extends nanobubble lifetimes.

Probing flow-induced nanostructure of complex fluids in arbitrary 2D flows using a fluidic four-roll mill (FFoRM).

Engineering flow processes to direct the microscopic structure of soft materials represents a growing area of materials research. In situ small-angle neutron scattering under flow (flow-SANS) is an attractive probe of fluid microstructure under simulated processing conditions, but current capabilities require many different sample environments to fully interrogate the deformations a fluid experiences in a realistic processing flow. Inspired by recent advances in microfluidics, we present a fluidic four-roll mill (FFoRM) capable of producing tunable 2D flow fields for in situ SANS measurements, that is intended to allow characterization of complex fluid nanostructure under arbitrary complex flows within a single sample environment. Computational fluid dynamics simulations are used to design a FFoRM that produces spatially homogeneous and sufficiently strong deformation fields. Particle tracking velocimetry experiments are then used to characterize the flows produced in the FFoRM for several classes of non-Newtonian fluids. Finally, a putative FFoRM-SANS workflow is demonstrated and validated through the characterization of flow-induced orientation in a semi-dilute cellulose nanocrystal dispersion under a range of 2D deformations. These novel experiments confirm that, for steady state straining flows at moderate strain rates, the nanocrystals orient along the principal strain-rate axis, in agreement with theories for rigid, rod-like Brownian particles in a homogeneous flow.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations.

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

Multiscale simulation of ideal mixtures using smoothed dissipative particle dynamics.

Smoothed dissipative particle dynamics (SDPD) [P. Español and M. Revenga, Phys. Rev. E 67, 026705 (2003)] is a thermodynamically consistent particle-based continuum hydrodynamics solver that features scale-dependent thermal fluctuations. We obtain a new formulation of this stochastic method for ideal two-component mixtures through a discretization of the advection-diffusion equation with thermal noise in the concentration field. The resulting multicomponent approach is consistent with the interpretation of the SDPD particles as moving volumes of fluid and reproduces the correct fluctuations and diffusion dynamics. Subsequently, we provide a general multiscale multicomponent SDPD framework for simulations of molecularly miscible systems spanning length scales from nanometers to the non-fluctuating continuum limit. This approach reproduces appropriate equilibrium properties and is validated with simulation of simple one-dimensional diffusion across multiple length scales.

Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics.

We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.

Direct measurement of interaction forces between charged multilamellar vesicles†.

Depletion-attraction induced adhesion of two giant (∼ 40 µm), charged multilamellar vesicles is studied using a new Cantilevered-Capillary Force Apparatus, developed in this laboratory. The specific goal of this work is to investigate the role of dynamics in the adhesion and de-adhesion processes when the vesicles come together or are pulled apart at a constant velocity. Hydrodynamic effects are found to play an important role in the adhesion and separation of vesicles at the velocities that are studied. Specifically, a period of hydrodynamically controlled drainage of the thin film between vesicles is observed prior to adhesion, and it is shown that the force required to separate a pair of tensed, adhering vesicles increases with increasing separation velocity and membrane tension. It is also shown that the work done to separate the vesicles increases with separation velocity, but exhibits a maximum as the membrane tension is varied.

Local, real-time measurement of drying films of aqueous polymer solutions using active microrheology.

Oscillatory microdisk rheometry was applied to evaluate the evolution of the viscoelastic properties at the surface of a film of an aqueous solution of poly(vinyl alcohol) (PVA) during drying. The drying rate was measured concurrently, based upon measurements of the variation of film thickness. A fully hydrolyzed PVA solution shows a constant drying rate, while a less hydrolyzed PVA solution exhibits a decreased drying rate in the latter part of the drying process, which occurred at the same time as an increase of the elastic modulus. We suggest that this difference in behavior is a consequence of the fact that both the configuration of the PVA molecule and the strength of interaction with water depend on the degree to which the PVA is hydrolyzed. The polymer concentration at the film surface can be estimated from the measured viscosity at the surface for the fully hydrolyzed PVA solution, and this result then can be compared with two theoretical calculations: one in which the polymer concentration is assumed to remain uniform throughout the film, and the other in which the polymer concentration distribution is determined via a one-dimensional diffusion model. This comparison suggests that the polymer is first concentrated locally near the surface but later in the drying process the distribution of polymer becomes increasingly uniform, possibly due to a spontaneously generated convective flow inside the film.

Surface shear inviscidity of soluble surfactants.

Foam and emulsion stability has long been believed to correlate with the surface shear viscosity of the surfactant used to stabilize them. Many subtleties arise in interpreting surface shear viscosity measurements, however, and correlations do not necessarily indicate causation. Using a sensitive technique designed to excite purely surface shear deformations, we make the most sensitive and precise measurements to date of the surface shear viscosity of a variety of soluble surfactants, focusing on SDS in particular. Our measurements reveal the surface shear viscosity of SDS to be below the sensitivity limit of our technique, giving an upper bound of order 0.01 µN·s/m. This conflicts directly with almost all previous studies, which reported values up to 10(3)-10(4) times higher. Multiple control and complementary measurements confirm this result, including direct visualization of monolayer deformation, for SDS and a wide variety of soluble polymeric, ionic, and nonionic surfactants of high- and low-foaming character. No soluble, small-molecule surfactant was found to have a measurable surface shear viscosity, which seriously undermines most support for any correlation between foam stability and surface shear rheology of soluble surfactants.

Origins of microstructural transformations in charged vesicle suspensions: the crowding hypothesis.

It is observed that charged unilamellar vesicles in a suspension can spontaneously deflate and subsequently transition to form bilamellar vesicles, even in the absence of externally applied triggers such as salt or temperature gradients. We provide strong evidence that the driving force for this deflation-induced transition is the repulsive electrostatic pressure between charged vesicles in concentrated suspensions, above a critical effective volume fraction. We use volume fraction measurements and cryogenic transmission electron microscopy imaging to quantitatively follow both the macroscopic and microstructural time-evolution of cationic diC18:1 DEEDMAC vesicle suspensions at different surfactant and salt concentrations. A simple model is developed to estimate the extent of deflation of unilamellar vesicles caused by electrostatic interactions with neighboring vesicles. It is determined that when the effective volume fraction of the suspension exceeds a critical value, charged vesicles in a suspension can experience "crowding" due to overlap of their electrical double layers, which can result in deflation and subsequent microstructural transformations to reduce the effective volume fraction of the suspension. Ordinarily in polydisperse colloidal suspensions, particles interacting via a repulsive potential transform into a glassy state above a critical volume fraction. The behavior of charged vesicle suspensions reported in this paper thus represents a new mechanism for the relaxation of repulsive interactions in crowded situations.

Adsorption energies of poly(ethylene oxide)-based surfactants and nanoparticles on an air-water surface.

The self-assembly of polymer-based surfactants and nanoparticles on fluid-fluid interfaces is central to many applications, including dispersion stabilization, creation of novel 2D materials, and surface patterning. Very often these processes involve compressing interfacial monolayers of particles or polymers to obtain a desired material microstructure. At high surface pressures, however, even highly interfacially active objects can desorb from the interface. Methods of directly measuring the energy which keeps the polymer or particles bound to the interface (adsorption/desorption energies) are therefore of high interest for these processes. Moreover, though a geometric description linking adsorption energy and wetting properties through the definition of a contact angle can be established for rigid nano- or microparticles, such a description breaks down for deformable or aggregating objects. Here, we demonstrate a technique to quantify desorption energies directly, by comparing surface pressure-density compression measurements using a Wilhelmy plate and a custom-microfabricated deflection tensiometer. We focus on poly(ethylene oxide)-based polymers and nanoparticles. For PEO-based homo- and copolymers, the adsorption energy of PEO chains scales linearly with molecular weight and can be tuned by changing the subphase composition. Moreover, the desorption surface pressure of PEO-stabilized nanoparticles corresponds to the saturation surface pressure for spontaneously adsorbed monolayers, yielding trapping energies of ∼10(3) k(B)T.

Direct measurements of effect of counterion concentration on mechanical properties of cationic vesicles.

Theoretical analyses of charged membranes in aqueous solutions have long predicted that the electric double layer surrounding them contributes significantly to their mechanical properties. Here we report the first, direct experimental measurements of the effect of counterion concentration on the bending and area expansion modulus of cationic surfactant vesicles. Using the classical technique of micropipet aspiration coupled with a modified experimental protocol that is better suited for cationic vesicles, we successfully measure the mechanical properties of a double-tailed cationic surfactant, diethylesterdimethyl ammonium chloride (diC18:1 DEEDMAC) in CaCl2 solutions. It is observed that the area expansion modulus of the charged membrane exhibits no measurable dependence on the counterion concentration, in accordance with existing models of bilayer elasticity. The measured bending modulus, however, is found to vary nonmonotonically and exhibits a minimum in its variation with counterion concentration. The experimental results are interpreted based on theoretical calculations of charged and bare membrane mechanics. It is determined that the initial decrease in bending modulus with increasing counterion concentration may be attributed to a decreasing double layer thickness, while the subsequent increase is likely due to an increasing membrane thickness. These mechanical moduli measurements qualitatively confirm, for the first time, theoretical predictions of a nonmonotonic behavior and the opposing effects of ionic strength on the bending rigidity of charged bilayers.

A test of systematic coarse-graining of molecular dynamics simulations: Transport properties.

To what extent can a "bottom-up" mesoscale fluid model developed through systematic coarse-graining techniques recover the physical properties of a molecular scale system? In a previous paper [C.-C. Fu, P. M. Kulkarni, M. S. Shell, and L. G. Leal, J. Chem. Phys. 137, 164106 (2012)], we addressed this question for thermodynamic properties through the development of coarse-grained (CG) fluid models using modified iterative Boltzmann inversion methods that reproduce correct pair structure and pressure. In the present work we focus on the dynamic behavior. Unlike the radial distribution function and the pressure, dynamical properties such as the self-diffusion coefficient and viscosity in a CG model cannot be matched during coarse-graining by modifying the pair interaction. Instead, removed degrees of freedom require a modification of the equations of motion to simulate their implicit effects on dynamics. A simple but approximate approach is to introduce a friction coefficient, γ, and random forces for the remaining degrees of freedom, in which case γ becomes an additional parameter in the coarse-grained model that can be tuned. We consider the non-Galilean-invariant Langevin and the Galilean-invariant dissipative particle dynamics (DPD) thermostats with CG systems in which we can systematically tune the fraction φ of removed degrees of freedom. Between these two choices, only DPD allows both the viscosity and diffusivity to match a reference Lennard-Jones liquid with a single value of γ for each degree of coarse-graining φ. This friction constant is robust to the pressure correction imposed on the effective CG potential, increases approximately linearly with φ, and also depends on the interaction cutoff length, rcut, of the pair interaction potential. Importantly, we show that the diffusion constant and viscosity are constrained by a simple scaling law that leads to a specific choice of DPD friction coefficient for a given degree of coarse-graining. Moreover, we find that the pair interaction distance cutoffs used for DPD random and dissipative forces should be considered separately from that of the conservative interaction potential.

Dynamic equilibrium explanation for nanobubbles' unusual temperature and saturation dependence.

The dynamic equilibrium model suggests that surface nanobubbles can be stable due to an influx of gas in the vicinity of the bubble contact line, driven by substrate hydrophobicity, that balances the outflux of gas from the bubble apex. Here, we develop an alternate formulation of this mechanism that predicts rich behavior in agreement with recent experimental measurements. Namely, we find that stable nanobubbles exist in narrow temperature and dissolved gas concentration ranges, that there is a maximum and minimum possible bubble size, and that nanobubble radii decrease with temperature.

Multiscale modeling with smoothed dissipative particle dynamics.

In this work, we consider two issues related to the use of Smoothed Dissipative Particle Dynamics (SDPD) as an intermediate mesoscale model in a multiscale scheme for solution of flow problems when there are local parts of a macroscopic domain that require molecular resolution. The first is to demonstrate that SDPD with different levels of resolution can accurately represent the fluid properties from the continuum scale all the way to the molecular scale. Specifically, while the thermodynamic quantities such as temperature, pressure, and average density remain scale-invariant, we demonstrate that the dynamic properties are quantitatively consistent with an all-atom Lennard-Jones reference system when the SDPD resolution approaches the atomistic scale. This supports the idea that SDPD can serve as a natural bridge between molecular and continuum descriptions. In the second part, a simple multiscale methodology is proposed within the SDPD framework that allows several levels of resolution within a single domain. Each particle is characterized by a unique physical length scale called the smoothing length, which is inversely related to the local number density and can change on-the-fly. This multiscale methodology is shown to accurately reproduce fluid properties for the simple problem of steady and transient shear flow.

Cantilevered-capillary force apparatus for measuring multiphase fluid interactions.

A new instrument is presented for investigating interactions between individual colloidal particles, emulsion droplets, foam bubbles, and other particle-particle or particle-surface interactions. Measurement capabilities are demonstrated by measuring interfacial tension, coalescence time for emulsion droplets, adhesion between giant multilamellar vesicles, and adhesion between model food emulsion particles. The magnitude of the interaction force that can be measured or imposed, ranges from 1 nN to 1 mN for particles ranging in size from 10 µm to 1 mm in diameter.

A test of systematic coarse-graining of molecular dynamics simulations: thermodynamic properties.

Coarse-graining (CG) techniques have recently attracted great interest for providing descriptions at a mesoscopic level of resolution that preserve fluid thermodynamic and transport behaviors with a reduced number of degrees of freedom and hence less computational effort. One fundamental question arises: how well and to what extent can a "bottom-up" developed mesoscale model recover the physical properties of a molecular scale system? To answer this question, we explore systematically the properties of a CG model that is developed to represent an intermediate mesoscale model between the atomistic and continuum scales. This CG model aims to reduce the computational cost relative to a full atomistic simulation, and we assess to what extent it is possible to preserve both the thermodynamic and transport properties of an underlying reference all-atom Lennard-Jones (LJ) system. In this paper, only the thermodynamic properties are considered in detail. The transport properties will be examined in subsequent work. To coarse-grain, we first use the iterative Boltzmann inversion (IBI) to determine a CG potential for a (1-φ)N mesoscale particle system, where φ is the degree of coarse-graining, so as to reproduce the radial distribution function (RDF) of an N atomic particle system. Even though the uniqueness theorem guarantees a one to one relationship between the RDF and an effective pairwise potential, we find that RDFs are insensitive to the long-range part of the IBI-determined potentials, which provides some significant flexibility in further matching other properties. We then propose a reformulation of IBI as a robust minimization procedure that enables simultaneous matching of the RDF and the fluid pressure. We find that this new method mainly changes the attractive tail region of the CG potentials, and it improves the isothermal compressibility relative to pure IBI. We also find that there are optimal interaction cutoff lengths for the CG system, as a function of φ, that are required to attain an adequate potential while maintaining computational speedup. To demonstrate the universality of the method, we test a range of state points for the LJ liquid as well as several LJ chain fluids.

Adhesive interactions between vesicles in the strong adhesion limit.

We consider the adhesive interaction energy between a pair of vesicles in the strong adhesion limit, in which bending forces play a negligible role in determining vesicle shape compared to forces due to membrane stretching. Although force−distance or energy−distance relationships characterizing adhesive interactions between fluid bilayers are routinely measured using the surface forces apparatus, the atomic force microscope, and the biomembrane force probe, the interacting bilayers in these methods are supported on surfaces (e.g., mica sheet) and cannot be deformed. However, it is known that, in a suspension, vesicles composed of the same bilayer can deform by stretching or bending, and can also undergo changes in volume. Adhesively interacting vesicles can thus form flat regions in the contact zone, which will result in an enhanced interaction energy as compared to rigid vesicles. The focus of this paper is to examine the magnitude of the interaction energy between adhesively interacting, deformed vesicles relative to free, undeformed vesicles as a function of the intervesicle separation. The modification of the intervesicle interaction energy due to vesicle deformability can be calculated knowing the undeformed radius of the vesicles, R0, the bending modulus, k(b), the area expansion modulus, k(a), and the adhesive minimum, W(P)(0), and separation, D(P)(0), in the energy of interaction between two flat bilayers, which can be obtained from the force−distance measurements made using the above supported-bilayer methods. For vesicles with constant volumes, we show that adhesive potentials between nondeforming bilayers such as |W(P)(0)| 5 × 10(−4) mJ/m2, which are ordinarily considered weak in the colloidal physics literature, can result in significantly deep (>10×) energy minima due to increase in vesicle area and flattening in the contact region. If the osmotic expulsion of water across the vesicles driven by the tense, stretched membrane in the presence of an osmotically active solute is also taken into account, the vesicles can undergo additional deformation (flattening), which further enhances the adhesive interaction between them. Finally, equilibration of ions and solutes due to the concentration differences created by the osmotic exchange of water can lead to further enhancement of the adhesion energy. Our result of the progressively increasing adhesive interaction energy between vesicles in the above regimes could explain why suspensions of very weakly attractive vesicles may undergo flocculation and eventual instability due to separation of vesicles from the suspending fluid by gravity. The possibility of such an instability is an extremely important issue for concentrated vesicle-based products and applications such as fabric softeners, hair therapeutics and drug delivery.

Dilution technique to determine the hydrodynamic volume fraction of a vesicle suspension.

A simple dilution method to determine the hydrodynamic volume fraction of vesicle suspensions is presented. The vesicle suspension is diluted with a solution containing a tracer Y, which is similar to a component X already present in the suspending fluid and which does not bind to or permeate through the vesicles. The concentrations of X and Y in the suspending fluid measured after dilution are used to determine the volume fraction. Using this technique, the volume fractions of vesicle suspensions comprising cationic vesicles prepared in solutions of CaCl(2) (X) were measured by dilution with MgCl(2) (Y) solutions. Various experimental parameters such as the concentration of the MgCl(2) diluents and the dilution volume ratio were studied and their effects optimized to arrive at a robust recipe for measuring the volume fraction. It is demonstrated that the technique can be applied to concentrated suspensions containing multilamellar and polydisperse vesicles.