A Langevin dynamics simulation study of the tribology of polymer loop brushes

The tribology of surfaces modified with doubly bound polymer chains (loops) has been investigated in good solvent conditions using Langevin dynamics simulations. The density profiles, brush interpenetration, chain inclination, normal forces, and shear forces for two flat substrates modified by doubly bound bead-necklace polymers and equivalent singly bound polymers (twice as many polymer chains of 12 the molecular weight of the loop chains) were determined and compared as a function of surface separation, grafting density, and shear velocity. The doubly bound polymer layers showed less interpenetration with decreasing separation than the equivalent singly bound layers. Surprisingly, this difference in interpenetration between doubly bound polymer and singly bound polymer did not result in decreased friction at high shear velocity possibly due to the decreased ability of the doubly bound chains to deform in response to the applied shear. However, at lower shear velocity, where deformation of the chains in the flow direction is less pronounced and the difference in interpenetration is greater between the doubly bound and singly bound chains, some reduction in friction was observed.     

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.     

Comparative PIV and LDA studies of Newtonian and non-Newtonian flows in an agitated tank

The paper presents results of an experimental study of the fluid velocity field in a stirred tank equipped with a Prochem Maxflo T (PMT) type impeller which was rotating at a constant frequency of N = 4.1 or 8.2 s^?1 inducing transitional (Re = 499 or 1307) or turbulent (Re = 2.43 × 10⁴) flow of the fluid. The experiments were performed for a Newtonian fluid (water) and a non-Newtonian fluid (0.2 wt% aqueous solution of carboxymethyl cellulose, CMC) exhibiting mild viscoelastic properties. Measurements were carried out using laser light scattering on tracer particles which follow the flow (2-D PIV). For both the water and the CMC solution one primary and two secondary circulation loops were observed within the fluid volume; however, the secondary loops were characterized by much lower intensity. The applied PMT-type impeller produced in the Newtonian fluid an axial primary flow, whilst in the non-Newtonian fluid the flow was more radial. The results obtained in the form of the local mean velocity components were in satisfactory agreement with the literature data from LDA. Distribution of the shear rate in the studied system was also analyzed. For the non-Newtonian fluid an area was computed where the elastic force dominates over the viscous one. The area was nearly matching the region occupied by the primary circulation loop.     

Constitutive equations for the flow behavior of entangled polymeric systems: application to star polymers

A semimicroscopic derivation is presented of equations of motion for the density and the flow velocity of concentrated systems of entangled polymers. The essential ingredient is the transient force that results from perturbations of overlapping polymers due to flow. A Smoluchowski equation is derived that includes these transient forces. From this, an equation of motion for the polymer number density is obtained, in which body forces couple the evolution of the polymer density to the local velocity field. Using a semimicroscopic Ansatz for the dynamics of the number of entanglements between overlapping polymers, and for the perturbations of the pair-correlation function due to flow, body forces are calculated for nonuniform systems where the density as well as the shear rate varies with position. Explicit expressions are derived for the shear viscosity and normal forces, as well as for nonlocal contributions to the body force, such as the shear-curvature viscosity. A contribution to the equation of motion for the density is found that describes mass transport due to spatial variation of the shear rate. The two coupled equations of motion for the density and flow velocity predict flow instabilities that will be discussed in more detail in a forthcoming publication.     

Nonequilibrium molecular dynamics of the rheological and structural properties of linear and branched molecules. Simple shear and poiseuille flows; instabilities and slip

Nonequilibrium molecular-dynamics simulations are performed for linear and branched chain molecules to study their rheological and structural properties under simple shear and Poiseuille flows. Molecules are described by a spring-monomer model with a given intermolecular potential. The equations of motion are solved for shear and Poiseuille flows with Lees and Edward's [A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972)] periodic boundary conditions. A multiple time-scale algorithm extended to nonequilibrium situations is used as the integration method, and the simulations are performed at constant temperature using Nose-Hoover [S. Nose, J. Chem. Phys. 81, 511 (1984)] dynamics. In simple shear, molecules with flow-induced ellipsoidal shape, having significant segment concentrations along the gradient and neutral directions, exhibit substantial flow resistance. Linear molecules have larger zero-shear-rate viscosity than that of branched molecules, however, this behavior reverses as the shear rate is increased. The relaxation time of the molecules is associated with segment concentrations directed along the gradient and neutral directions, and hence it depends on structure and molecular weight. The results of this study are in qualitative agreement with other simulation studies and with experimental data. The pressure (Poiseuille) flow is induced by an external force F(e) simulated by confining the molecules in the region between surfaces which have attractive forces. Conditions at the boundary strongly influence the type of the slip flow predicted. A parabolic velocity profile with apparent slip on the wall is predicted under weakly attractive wall conditions, independent of molecular structure. In the case of strongly attractive walls, a layer of adhered molecules to the wall produces an abrupt distortion of the velocity profile which leads to slip between fluid layers with magnitude that depends on the molecular structure. Finally, the molecular deformation under flow depends on the attractive force of the wall, in such a way that molecules are highly deformed in the case of strong attracting walls.     

Extensional flow of bulk polymers studied by dynamic Monte Carlo simulations

Dynamic Monte Carlo simulations of bulk lattice polymers driven through planar geometries with sequentially converging,parallel and diverging spaces between two neutrally repulsive solid plates are reported.The spatial profiles of polymer velocity and deformation along the course of such a laminar extensional flow have been carefully analyzed.The results appear consistent with experimental observations in literature.In the entrance and exit regions,a linear dependence of chain extension upon the excess velocity has been observed.Moreover,an annexed shear flow and a molecular-dispersion effect are found.The results demonstrate a useful strategy of this approach to study polymer flows and bring new insights into the non-Newtonian-fluid behaviors of bulk polymers in capillary rheometers and micro-fluidic devices.     

Electrokinetic diffusioosmotic flow of Ostwald-de Waele fluids near a charged flat plate in the thin double layer limit

Electrokinetic diffusioosmotic flow of Ostwald-de Waele, or power-law, fluids near a large charged flat plate is theoretically investigated for very thin double layers. Solutions to the flow velocity both up-close and far from the flat plate as well as the effective viscosity are presented for general values of the flow behavior index. Results show that given a wall zeta potential, ζ, diffusivity difference parameter, β, and constant imposed solute concentration gradient, both the near and far field diffusioosmotic flow velocities obtained for the respective dilatant and pseudoplastic liquids considerably deviate from those obtained for Newtonian liquids as found in previous literature. This likely suggests that the electrokinetic diffusioosmosis and its complementary effect of diffusiophoresis depend sensitively not only on the ζ-β parametric pair, but also on the possible non-Newtonian characteristics of the electrolytic liquid phase of the system. The theory presented herein can also be readily modified to model or describe electrodiffusioosmosis in power-law fluids, which is likely found in flow situations where the fluid non-Newtonian response, imposed solute concentration gradient, and an additional externally applied electric current density (or electric field) are of equal importance.     

Dynamic wetting of Boger fluids

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Ramé, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a "solvent" of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.     

Rheological peculiarities of concentrated suspensions

The rheological properties of concentrated suspensions of metal oxides dispersed in transformer oil, which are used as electrorheological fluids, are systematically studied. Colloidal particles have intermediate sizes between nano- and microsized scales. Low-amplitude dynamic measurements show that the storage moduli of the examined suspensions are independent of frequency and these materials should be considered as solidlike elastic media. The storage modulus is proportional to the five-powdered particle volume concentration. At the same time, a transition through an apparent yield stress with a reduction in the viscosity by approximately six orders of magnitude is distinctly seen upon shear deformation. The character of the rheological behavior depends on the regime of suspension deformation. At very low shear rates, a steady flow is possible; however, upon an increase in the rate, an unsteady regime is realized with development of self-oscillations. When constant shear stresses are preset, in some range of stresses, thickening of the medium takes place, which can also be accompanied by self-oscillations. In order to gain insight into the nature of this effect, measurements are performed for samples with different volume/surface ratios, which show that, in some deformation regimes, suspension is separated into layers and slipping occurs along a low-viscosity layer with a thickness of several dozen microns. Direct observations show a distinct structural inhomogeneity of the flow. The separation and motion of layers with different compositions explain the transition to the flow with the lowest apparent Newtonian viscosity. Thus, the deformation of concentrated suspensions is associated with self-oscillations of stresses and slipping along a low-viscosity interlayer.     

Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

Statistical-mechanical theory of rheology: Lennard-Jones fluids

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a suitable flow configuration. The non-Newtonian viscosity formula derived is applied to calculate the non-Newtonian viscosity as a function of the shear rate by means of statistical mechanics in the case of the Lennard-Jones fluid. For that purpose we have used the density-fluctuation theory for the Newtonian viscosity, the modified free volume theory for the self-diffusion coefficient, and the generic van der Waals equation of state to compute the mean free volume appearing in the modified free volume theory. Monte Carlo simulations are used to calculate the pair-correlation function appearing in the generic van der Waals equation of state and shear viscosity formula. To validate the Newtonian viscosity formula obtained we first have examined the density and temperature dependences of the shear viscosity in both subcritical and supercritical regions and compared them with molecular-dynamic simulation results. With the Newtonian shear viscosity and thermodynamic quantities so computed we then have calculated the shear rate dependence of the non-Newtonian shear viscosity and compared it with molecular-dynamics simulation results. The non-Newtonian viscosity formula is a universal function of the product of reduced shear rate (gamma*) times reduced relaxation time (taue*) that is independent of the material parameters, suggesting a possibility of the existence of rheological corresponding states of reduced density, temperature, and shear rate. When the simulation data are reduced appropriately and plotted against taue*gamma* they are found clustered around the reduced (universal) non-Newtonian viscosity formula. Thus we now have a molecular theory of non-Newtonian shear viscosity for the Lennard-Jones fluid, which can be implemented with a Monte Carlo simulation method for the pair-correlation function.     

Strain-Dependent Rheological Model and Pressure Wave Prediction for Shut in and Restart of Waxy Oil Pipelines

Waxy oil gelation and rheology is investigated and modeled using strain-dependent viscosity correlations. Rotational rheometry shows a sharp viscosity increase upon gel formation. High creeping flow viscosities are observed at small deformation conditions prior to yielding. A new strain-dependent rheological model, following analogous formulation to the Carreau–Yasuda shear rate-dependent model, captures viscosity reduction associated with yielding. In addition, shear viscosity and extensional viscosity are investigated using a capillary rheometry method. Distinct shear-thinning behavior is observed in the shear mode of deformation, while distinct tension-thinning behavior is observed in the extensional mode of deformation for the model fluid systems. High Trouton ratios are obtained for the gelled model fluid systems, confirming strongly non-Newtonian fluid rheology. Finally, axial pressure wave profiles are computed at real pipeline dimensions for idealized moderate yield stress fluids using a computationally efficient 1D pipeline simulator. The Rønningsen time-dependent gel degradation model is used to emulate the fluid rheology in the simulator. Axial stress localization phenomena are shown to depend on the overall magnitude of gel degradation as established by the reduction in yield value. A high degree of gel degradation serves to afford flow commencement in a timely manner.     

Modified graessley theory for non-newtonian viscosities of polydimethylsiloxanes and their solutions

A deviation from Graessley's theory of entanglement viscosity appears at very high shear rates when the flow of polydimethylsiloxanes of various molecular weights and their solutions with various concentrations is measured by the capillary method. In order to explain this deviation, a modified Graessley theory is proposed according to the previously reported suggestion that frictional viscosity appears not to be negligible at high shear rates. A reducing procedure taking a frictional viscosity parameter into account was performed. All of the reduced data are combined to give a master curve in spite of a wide range of molecular weight, concentration, and shear rate (from the lower Newtonian to very highest non-Newtonian flow region). The findings from the reducing procedure completely explain the mechanism of non-Newtonian flow for the bulk polymers with various molecular weights, including those below the critical molecular weight for entanglement, and for polymer solutions at any concentration. The viscosity of the linear polymer system consists of the shear-dependent entanglement term η_ent proposed by Graessley and the shear-independent frictional term η_fric. The non-Newtonian behavior depends on the ratio of η_ent/η_fric at the shear rate of measurement. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric and the critical shear rate for onset of the non-Newtonian flow may be used as a measure of the non-Newtonian behavior of the system and a measure of capability for its rising, respectively. The Graessley theory is to be included in the present modified theory and is applicable to the case of η_entη_fric ? 1.     

Flow-induced shear stress and deformation of a core–shell-structured microcapsule in a microchannel

A numerical model was developed and validated to investigate the fluid–structure interactions between fully developed pipe flow and core–shell-structured microcapsule in a microchannel. Different flow rates and microcapsule shell thicknesses were considered. A sixth-order rotational symmetric distribution of von Mises stress over the microcapsule shell can be observed on the microcapsule with a thinner shell configuration, especially at higher flow rate conditions. It is also observed that when being carried along in a fully developed pipe flow, the microcapsule with a thinner shell tends to accumulate stress at a higher rate compared to that with a thicker shell. In general, for the same microcapsule configuration, higher flow velocity would induce a higher stress level over the microcapsule shell. The deformation gradient was used to capture the microcapsule's deformation in the present study. The effect of Young's modulus on the microcapsule shell on the microcapsule deformation was investigated as well. Our findings will shed light on the understanding of the stability of core–shell-structured microcapsule when subjected to flow-induced shear stress in a microfluidic system, enabling a more exquisite control over the breakup dynamics of drug-loaded microcapsule for biomedical applications.     

部分水解聚丙烯酰胺与蠕虫状胶束在微米级毛细管中的驱替粘度

部分水解聚丙烯酰胺(HPAMs)被大量地用作三次采油中驱替液的增稠剂,表面活性剂在一定的条件下可以通过自组装形成蠕虫状胶束,具有与高分子相似的增稠的作用。本文在半径为1–10 μm的毛细管中,分别考察了HPAMs与蠕虫状胶束的微观驱替行为,研究结果表示毛细管内腔的尺寸限制了这些非牛顿流体的增稠作用。随着毛细管半径的减小,聚合物溶液的剪切变稀越剧烈,甚至从非牛顿流体转变为牛顿流体的流体行为。结合驱替研究和超滤、电镜的结果,证明了高分子的缠绕结构在毛细管中已被破坏。通过对比驱替数据,蠕虫状胶束在毛细管中能够更大程度地保留宏观的粘度,我们提出表面活性剂能够通过自组装修复被破坏的缠绕结构,比高分子聚合物在微观有限空间中有更好的增稠能力。     

Analysis of the shape of dendrimers under shear

Nonequilibrium molecular-dynamics simulations are used to investigate the molecular shape of dendrimers and linear polymers in a melt and under shear. Molecules are modeled at the coarse-grained level using a finitely extensible nonlinear elastic bead-spring model. The shape of dendrimers and linear polymers at equilibrium and undergoing planar Couette flow is analyzed quantitatively and it is related to the shear viscosity. The shape of dendrimers responds differently to the influence of shear compared with linear polymers of equivalent molecular mass. However, in both cases the transition from Newtonian to non-Newtonian viscosity behavior corresponds to significant changes in molecular symmetry. This suggests that a shape analysis could be used to estimate the onset of shear thinning in polymers.     

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here:First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.     

Influence of nozzle geometry on polystyrene degradation in convergent flow

Polymer degradation is readily observed in flows where the extensional component surpasses the rotational component of the velocity gradient. This type of flow is conveniently obtained by pushing a liquid into a convergent channel across an orifice. Kinetics of chain scission is sensitive to subtle modification of the coil conformation, which in turn depends on the details of the pervading flow field. By changing the orifice diameter and the conical angle of the inlet, it is possible to modify the spatial distribution of the velocity gradient, and hence, the residence time of a fluid element in the high strain-rate region. Degradation yields, measured under -conditions in decalin by Gel Permeation Chromatography, showed a strong dependence on the fluid velocity at the orifice, but not on the magnitude of the strain-rate. This result is contrary to the common belief that assumes viscous friction, proportional to the strain-rate, is the determining factor for the scission rate of a bond under stress. Rather, experimental findings tend to indicate that the driving force for chain scission was provided by the energy accumulated in the coil during the flow-induced deformation process. The sharp propensity for mid-chain scission was maintained regardless of the nozzle geometry.Dedicated to Prof. W. R. Pechhold on the occasion of his 60th birthday     

On the Stagnation Point Flow of a Special Class of Non-Newtonian Fluids

Abstract

The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.     

Analytical solutions for velocity, temperature and concentration distribution in electroosmotic microchannel flows of a non-Newtonian bio-fluid

In this paper, analytical solutions are derived, describing the transport characteristics of a non-Newtonian fluid flow in a rectangular microchannel, under the sole influence of electrokinetic forces. Apart from estimating the fully-developed velocity and temperature distributions, an explicit expression is derived for solutal concentration distribution within the microchannel. Finally, as an illustrative case study, the flow behaviour of a blood sample is analyzed, in which the flow parameters are modeled as functions of the hematocrit fraction in the sample. It is revealed that a higher hematocrit fraction may result in significant reductions in species concentration levels, on account of stronger dispersions in the velocity profiles, characterized by more significant viscous effects. It is also demonstrated that cases in which characteristic length scale of RBC suspensions turns out to be consequential relative to the microchannel dimensions, a significant augmentation in the electroosmotic transport may occur. Such observations can be of particular significance in the design of electroosmotically actuated bio-microfluidic systems as efficient solutal carriers.