Bamin Khomami

Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues

Abstract The efficiency and robustness of various numerical schemes have been evaluated by performing Brownian dynamics simulations of bead-rod and three popular nonlinear bead-spring chain models in uniaxial extension and simple shear flow. The bead-spring models include finitely extensible nonlinear elastic (FENE) springs, worm-like chain (WLC) springs, and Pade approximation to the inverse Langevin function (ILC) springs. For the bead-spring chains two new predictor–corrector algorithms are proposed, which are much superior to commonly used explicit and other fully implicit schemes. In the case of bead-rod chain models, the mid-point algorithm of Liu [J. Chem. Phys. 90 (1989) 5826] is found to be computationally more efficient than a fully implicit Newton’s method. Furthermore, the accuracy and computational efficiency of two different stress expressions for the bead-rod chains, namely the Kramers–Kirkwood and the modified Giesekus have been evaluated under both transient and steady conditions. It is demonstrated that the Kramers–Kirkwood with stochastic filtering is the preferred choice for transient flow while the Giesekus expression is better suited for steady state calculations. The issue of coarse graining from a bead-rod chain to a bead-spring chain has also been investigated. Though bead-spring chains are shown to capture only semi-quantitatively the response of the bead-rod chains in transient flows, a systematic coarse-graining procedure that provides the best description of bead-rod chains via bead-spring chains is presented.

An experimental investigation of interfacial instabilities in multilayer flow of viscoelastic fluids: Part I. Incompatible polymer systems

Abstract The interfacial stability of coextruded polypropylene (PP) and high-density polyethylene (HDPE) has been examined experimentally in a slit-die geometry. Our experimental apparatus makes use of a novel system for introducing temporally regular disturbances with a controllable amplitude and frequency. The growth or decay of the disturbance can be observed via optical windows mounted in the test die and characterized with the aid of digital image-processing techniques. This approach has allowed us to construct experimentally determined stability and growth-rate plots as a function of disturbance wavenumber and layer-depth ratio. Our experimental results are compared to theoretical results based on the linear stability analysis using a modified Oldroyd-B equation. We have found this model to be quantitatively correct in its prediction of the critical layer-depth ratio and the existence of a maximum spatial growth rate in the vicinity of a dimensionless wavenumber of one. The theoretically predicted growth rates agree with our experimental data at low wavenumbers but fail to agree at higher wavenumbers. Overall, our findings provide evidence that in order to achieve quantitative agreement between theoretical and experimental results, a constitutive model should be utilized that accounts for the shear-rate dependence of first and second normal stresses and a spectrum of relaxation times.

An experimental investigation of interfacial instabilities in multilayer flow of viscoelastic fluids. Part II. Elastic and nonlinear effects in incompatible polymer systems

Superposed plane Poiseuille flow of an incompatible polymer system consisting of polypropylene and high‐density polyethylene has been investigated. Using the apparatus and procedures developed in our previous study [G. M. Wilson and B. Khomami J. Non‐Newt. Fluid Mech. 45, 355 (1992)], we have investigated the role of elasticity in interfacial stability, the existence of subcritical and supercritical bifurcations and the combined effects of interfacial instability and layer encapsulation. We have confirmed experimentally that elasticity plays a key role in the interfacial stability problem. Concerning the existence of bifurcations, we did not find any subcritical bifurcations in the parameter range of our study while supercritical bifurcations accompanied by highly elongated and bent interfacial waves were observed. Our investigation of the combined effects of layer‐to‐layer encapsulation and interfacial instability has revealed that the two phenomena will couple resulting in complex three‐dimensional wave...

Interfacial stability of multilayer viscoelastic fluids in slit and converging channel die geometries

Interfacial stability of stratified Oldroyd‐B liquids with constant and shear rate dependent viscosity in slit and converging channel die geometries has been examined by utilizing both asymptotic and numerical techniques. To elucidate the mechanisms by which shear thinning viscosity and elasticity influence interfacial stability, neutral stability contours in the parametric space of viscosity, depth, and elasticity ratio as well as interfacial tension and Reynolds number have been constructed. Our results indicate that elasticity and viscosity stratification as well as inertial forces affect the stability of the interface at all disturbance wavelengths. Moreover, it is found that neutral stability contours are substantially altered in converging channel flows. Overall, our analysis indicates that under certain physical (i.e., viscosity and elasticity ratio) and geometric conditions (i.e., depth ratio and channel convergence) stable regions at all disturbance wavelengths can be attained. Hence, based on th...

Application of higher order finite element methods to viscoelastic flow in porous media

A higher order Galerkin finite element scheme for simulation of two‐dimensional viscoelastic fluid flows has been developed. The numerical scheme used in this study gives rise to a stable discretization of the continuum problem as well as providing an exponential convergence rate toward the exact solution. Hence, with this method, spurious oscillatory modes are effectively eliminated by increasing the order of the interpolant within each subdomain. In our calculations, an upper limit for the Weissenberg number due to numerical instability was not encountered. However, the memory requirements of the discretization grow quadratically with the polynomial order. Consequently, the maximum attainable We is determined by the availability of computational resources. The algorithm was tested for flow of upper convected Maxwell and Oldroyd‐B fluids in the undulating tube problem and it was subsequently applied to viscoelastic flow past square cylindrical arrangements. The results obtained show no increase in the fl...

Polymeric flow through fibrous media

Proper description of the resin flow through fibrous media is a very important input in the modeling of composite manufacturing processes. In this study, the complex phenomena associated with the flow of viscoelastic fluids through fibrous media are examined. In particular, the effects of fluid and fiber bed properties on the pressure drop observed during such flows were investigated, in conjunction with the specific conditions of typical composite manufacturing processes. To gain some insight into the problem, a theoretical and experimental investigation of Newtonian and non‐Newtonian flows through different geometric cylinder arrangements designed to simulate the actual fiber configurations was carried out. Particular care was taken to select the appropriate dimensionless flow parameters to demonstrate that the onset of the ‘‘excess’’ pressure drop due to fluid elasticity is independent of the flow geometry. Employment of this dimensionless group, which is related to the total strain on the macromolecul...

Irreversible nanogel formation in surfactant solutions by microporous flow

Self-assembly of surfactant molecules into micelles of various shapes and forms has been extensively used to synthesize soft nanomaterials. Translucent solutions containing rod-like surfactant micelles can self-organize under flow to form viscoelastic gels. This flow-induced structure (FIS) formation has excited much fundamental research and pragmatic interest as a cost-effective manufacturing route for active nanomaterials. However, its practical impact has been very limited because all reported FIS transitions are reversible because the gel disintegrates soon after flow stoppage. We present a new microfluidics-assisted robust laminar-flow process, which allows for the generation of extension rates many orders of magnitude greater than is realizable in conventional devices, to produce purely flow-induced permanent nanogels. Cryogenic transmission electron microscopy imaging of the gel reveals a partially aligned micelle network. The critical flow rate for gel formation is consistent with the Turner-Cates fusion mechanism, proposed originally to explain reversible FIS formation in rod-like micelle solutions.

Modeling of viscoelastic lid driven cavity flow using finite element simulations

Abstract In this study we have used a convergent and highly accurate mixed finite element technique to model the effect of fluid elasticity on the flow kinematics and the stress distribution in lid driven cavity flow. Our work is motivated by the desire to capture the important physical aspects of the basic flow and thus to better understand the purely elastic instability in recirculating flows which has been reported in the literature elsewhere [A.M. Grillet, E.S.G. Shaqfeh, Observations of viscoelastic instabilities in recirculation flows of Boger fluids, J. Non-Newtonian Fluid Mech. 64 (1996) 141–155; P. Pakdel, G.H. McKinley, Cavity flows of elastic liquids: purely elastic instablities, Phys. Fluids 10 (5) (1998) 1058–1070]. In our numerical investigations we have treated the corner singularities by incorporating a controlled amount of leakage which allows the computation of fully elastic mesh converged solutions. We begin by validating our Newtonian cavity results against previous work to show that the introduction of leakage does not appreciably modify the cavity recirculation flow. Then we examine the polymer stresses to understand how elasticity changes the flow kinematics, slowing the primary recirculation vortex and causing the vortex center to shift opposite of the direction of lid motion. Variations of the cavity aspect ratio are also explored. Focusing on the corners we find that the leakage relieves the corner singularities and moreover, finite leakage helps explain the unusual behavior seen in the radial velocity in experiments. Finally, we have reexamined the previously proposed mechanisms for elastic instability in this flow and put forth a new instability mechanism. Together, these mechanisms may better explain the complex aspect ratio dependence of the onset of elastic instability in lid driven cavity flow.

Interfacial stability and deformation of two stratified power law fluids in plane poiseuille flow Part I. Stability analysis

Abstract The interface stability of two stratified power law fluids in plane Poiseuille flow is considered. Stability diagrams are given in terms of viscosity and depth ratios as a function of power law indices. The work of previous investigators for two Newtonian and second-order fluids has been generalized and presented in a similar fashion. It is found that dependence of viscosity on shear rate has a pronounced effect on the interfacial stability regime in a more drastic manner than of an effective viscosity change. Furthermore, it is found that for power law fluids the effect of shear thinning viscosity in the less viscous fluid mainly affects the stability region for viscosity ratios less than unity, while for viscosity ratios greater than unity shear thinning in both layers affects the stability regime, particularly at small depth ratios.

Purely elastic interfacial instabilities in superposed flow of polymeric fluids

Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.