Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

This work presents experimental results on simple shear and porous media flow of aqueous solutions of two hydroxyethyl celluloses (HEC) and two hydrophobically modified hydroxyethyl celluloses (HMHEC) with different molecular weights. Mixtures of these polymers with a cationic surfactant, cetyltrimethylammonium p-toluenesulfonate (CTAT) were also studied. Emphasis was given to the range of surfactant concentrations in which wormlike micelles are formed. The presence of hydrophobic groups, the effect of the molecular weight of the polymers, the surfactant and polymer concentrations, and the effect of the flow field type (simple shear versus porous media flow) were the most important variables studied. The results show that the shear viscosity of HEC/CTAT solutions is higher than the viscosities of surfactant and polymer solutions at the same concentrations, but surface tension measurements indicate that no complex formation occurs between CTAT and HEC. On the other hand, a complex driven by hydrophobic interactions was detected by surface tension measurements between CTAT and HMHEC. In this case, the viscosity of the mixture increases significantly more (up to four orders of magnitude at high CTAT concentrations) in comparison with HEC/CTAT aqueous solutions. Increments in the molecular weight of the polymers increase the interaction with CTAT and the shear viscosity of the solution, but make phase separation more feasible. In porous media flow, the polymer/CTAT mixtures exhibited higher apparent viscosities than in simple shear flows. This result suggests that the extensional component of the flow field in porous media flows leads to a stronger interaction between the polymer and the wormlike micelles, probably as a consequence of change of conformation and growth of the micelles.     

Effect of ionic strength on the rheological behavior of aqueous cetyltrimethylammonium p-toluene sulfonate solutions

The influence of ionic environment on the rheological properties of aqueous cetyltrimethylammonium p-toluene sulfonate (CTAT) solutions has been studied under three different flow fields: simple shear, opposed-jets flow and porous media flow. Emphasis was placed in the experiments on a range of CTAT concentration in which wormlike micelles were formed. It is known that these solutions exhibit shear thickening in the semi-dilute regime, which has been explained in terms of the formation of shear-induced, cooperative structures involving wormlike micelles. In simple shear flow, the zero shear viscosity exhibits first an increase with salt addition followed by a decrease, while the critical shear rate for shear thickening increases sharply at low salt contents and tends to saturate at relatively high ionic strengths. The results are explained in terms of a competition between micellar growth induced by salt addition and changes in micellar flexibility caused by ionic screening effects. Dynamic light scattering results indicate that micelles grow rapidly upon salt addition but eventually achieve a constant size under static conditions. These observations suggest that the wormlike micelles continuously grow with salt addition, but, as they become more flexible due to electrostatic screening, the wormlike coils tend to adopt a more compact conformation. The trends observed in the apparent viscosities measured in porous media flows seem to confirm these hypotheses-but viscosity increases in the shear thickening region-and are magnified by micelle deformation induced by the elongational nature of the local flow in the pores. In opposed-jets flow, the solutions have a behavior that is close to Newtonian, which suggests that the range of strain rates employed makes the flow strong enough to destroy or prevent the formation of cooperative micellar structures.     

Microfluidic flows of wormlike micellar solutions

The widespread use of wormlike micellar solutions is commonly found in household items such as cosmetic products, industrial fluids used in enhanced oil recovery and as drag reducing agents, and in biological applications such as drug delivery and biosensors. Despite their extensive use, there are still many details about the microscopic micellar structure and the mechanisms by which wormlike micelles form under flow that are not clearly understood. Microfluidic devices provide a versatile platform to study wormlike micellar solutions under various flow conditions and confined geometries. A review of recent investigations using microfluidics to study the flow of wormlike micelles is presented here with an emphasis on three different flow types: shear, elongation, and complex flow fields. In particular, we focus on the use of shear flows to study shear banding, elastic instabilities of wormlike micellar solutions in extensional flow (including stagnation and contraction flow field), and the use of contraction geometries to measure the elongational viscosity of wormlike micellar solutions. Finally, we showcase the use of complex flow fields in microfluidics to generate a stable and nanoporous flow-induced structured phase (FISP) from wormlike micellar solutions. This review shows that the influence of spatial confinement and moderate hydrodynamic forces present in the microfluidic device can give rise to a host of possibilities of microstructural rearrangements and interesting flow phenomena.     

Shear and extensional rheology of solutions of mixtures of poly(ethylene oxide) and anionic surfactants in ionic environments

Interactions between a high molecular weight poly(ethylene oxide) (PEO) and the anionic surfactant sodium dodecyl benzene sulfonate (SDBS) in aqueous solutions were investigated by shear and extensional rheometry. Results for mixtures between PEO and sodium dodecyl sulfate (SDS) are also presented for comparison purposes. Addition of anionic surfactants to PEO solutions above the critical aggregation concentration (CAC), at which micellar aggregates attach to the polymer chain, results in an increase in shear viscosity due to PEO coil expansion, and a strengthening of interchain interactions. In extensional flows, these interactions result in a decrease of the critical shear rate for the onset of the characteristic extension thickening of the PEO solutions that is due to transient entanglements of polymer molecules. The relaxation times associated with these transient entanglements are not directly proportional to the shear viscosity of the solutions, but rather vary more rapidly with surfactant concentration. In the presence of an electrolyte, coil contraction results in lower shear viscosities and a decrease in the extension thickening effects at surfactant concentrations just beyond the CAC. The relaxation times associated with transient entanglement reach a minimum at the same surfactant concentration as the shear viscosity, which indicates that coil contraction is responsible for the observed effects in both types of flow. However, the increase in extensional-flow entanglement relaxation times is much more abrupt than the decrease in shear viscosity. All these results point to a greater sensitivity of extensional flows on the molecular conformation of PEO/surfactant complexes.     

Shear rheology and porous media flow of wormlike micelle solutions formed by mixtures of surfactants of opposite charge

The rheology of solutions of wormlike micelles formed by oppositely charged surfactant mixtures (cationic cetyl trimethylammonium p-toluene sulfonate, CTAT, and anionic sodium dodecyl sulfate, SDS), in the dilute and semi-dilute regimes, were studied under simple shear and porous media flows. Aqueous mixtures of CTAT and SDS formed homogeneous solutions for SDS/CTAT molar ratios below 0.12. Solutions of mixtures exhibited a strong synergistic effect in shear viscosity, especially in the semi-dilute regime with respect to wormlike micelles, reaching a four order of magnitude increase in the zero-shear rate viscosity for solutions with 20 mM CTAT. Oscillatory shear results demonstrated that the microstructure of CTAT wormlike micelles is sensitive to SDS addition. The cross-over relaxation times of wormlike micelles of 20 mM CTAT solutions increased by three orders of magnitude with the addition of up to 2 mM of SDS, and the solutions became increasingly elastic. The shear thickening process observed in shear rheology became more pronounced in porous media flow due to the formation of stronger cooperative structures induced by the extensional component of the flow.     

Nonlinear rheology of CTAB/NaSal aqueous solutions: finite extensibility of a network of wormlike micelles

The nonlinear rheology of aqueous solutions of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) was investigated. The concentration of CTAB was fixed at 0.1 mol L(-1), and the concentration of NaSal was varied from 0.07 to 0.4 mol L(-1). For all test solutions, dynamic moduli were described with the Maxwell model having a single relaxation time, tau. Time evolutions of the shear stress, sigma, and the first normal stress difference, N(1), after inception of the steady shear flow were measured. For solutions having low NaSal concentrations, strain-hardening was observed and sigma and N(1) diverged at a certain strain when the shear rate, , exceeded tau(-1). For solutions with high NaSal concentrations, stress overshoot similar to that of ordinary entangled polymer solutions was observed at between tau(-1) and a certain critical rate, (C), while the strain-hardening was observed at > (C). A simple relationship for elastic solids, N(1)/sigma = gamma with gamma being the strain imposed by shear flow, held for all the solutions in the strain-hardening regime. The strain-hardening was attributable to the strain-dependent shear modulus and well described with the network theory considering the finite extensibility of network strands. The segment size of network strands was successfully determined. Thus, the stress-strain relationship obtained after the inception of fast flows is useful for characterizing the network properties.     

Probing the molecular-scale lipid bilayer response to shear flow using nonequilibrium molecular dynamics

A nonequilibrium molecular dynamics simulation of the response of dimyristoylphosphatidylcholine (DMPC) bilayers to a solvent shear flow is presented. Application of shear flow to planar, stationary DMPC bilayers results in a redistribution of the membrane density profile along the bilayer normal due to the alignment of the lipids in the direction of flow and an increase in average lipid chain length. An increase in the intermolecular and intramolecular order of the lipids in response to the shear flow is also observed. This study provides groundwork for understanding the mechanism of the full response of lipid bilayers to externally imposed solvent shear flows, beginning with the response in the absence of collective lipid motions such as undulations and bilayer flow.     

Influence of an electric field on the non-Newtonian response of a hybrid-aligned nematic cell under shear flow

The authors study shear flow in hybrid-aligned nematic cells under the action of an applied electric field by solving numerically a hydrodynamic model. The authors apply this model to a flow-aligning nematic liquid crystal (4'-n-pentyl-4-cyanobiphenyl) and obtain the director's configuration and the velocity profile at the stationary state. The authors calculate the local and apparent viscosities of the system and found that the competition between the shear flow and the electric field gives rise to an interesting non-Newtonian response with regions of shear thickening and thinning. The results also show an important electrorheological effect ranging from a value a bit larger than the Miesowicz viscosity etab [Nature (London) 17, 261 (1935)] for small electric fields and large shear flows to etac for large electric fields and small shear flows. The analysis of the first normal stress difference shows that for small negative shear rates, the force between the plates of the cell is attractive, while it is repulsive for all other values of shear rates. However, under the application of the electric field, one can modify the extent of the region of attraction. Finally, the authors have calculated the dragging forces on the plates of the cell and found that it is easier to shear in one direction than in the other.     

Planar mixed flow and chaos: Lyapunov exponents and the conjugate-pairing rule

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.     

A constitutive equation derived from the model of doi and edwards for concentrated polymer solutions and polymer melts

In deriving a constitutive equation from a molecular model of polymers in concentrated solutions and melts, Doi and Edwards used a mathematical approximation, the “independent alignment approximation,” which has recently been shown to produce significant error in the particular case of stress relaxation following a double-step strain in opposite direction. In the present paper, in order to examine the approximation in general cases, we derive a new constitutive equation without using the independent alignment approximation. The new equation is a nonlinear integro-differential equation and is solved numerically for several cases, i.e., steady shear and elongational flows, and the transient flows after the start of shear and elongation. It is found that, in the cases examined here, the new constitutive equation gives nearly the same results as the old one: the rheological functions calculated from the two theories differ no more than 30%. This substantiates the expectation that the independent alignment approximation does not produce drastic error as long as the flow direction is not reversed.     

Localized flow birefringence of polyethylene oxide solutions in a four roll mill

We report flow birefringence observations of polyethylene oxide solutions in a four roll mill where the flow field in the central region of the mill approximates well to that of pure shearing flow. When flow birefringence is observed it is seen to be highly localized within a region close to the “outgoing” asymptotic plane of flow. The phenomenon can be explained in terms of the flow birefringence corresponding to high extension of some polymer chains where the localization is caused by the chains requiring sufficient time in the flow field to become extended. This explanation has important consequences in all “persistently extensional flows” and can explain the origin of previously published results of localized flow birefringence observed for polyethylene solutions in axial compression and axial extensional flows.     

Stress jumps on weakly flocculated dispersions: steady state and transient results

Weakly flocculated, thixotropic suspensions have been investigated by means of fast stress jump experiments. With a suitable procedure, reliable stress relaxation data could be collected starting 20 ms after cessation of flow. This technique has been used to determine the elastic and hydrodynamic contributions to the shear stress. Steady state as well as transient flows have been studied for suspensions containing either fumed silica or carbon black particles in a Newtonian medium. In both systems, the elastic stress totally dominates the response at low shear rates and consequently also the apparent yield stress. This stress contribution becomes negligibly small at high shear rates. The hydrodynamic contribution to the viscosity has finite limits at both the low and high shear rate ends. The data are relevant for testing rheological models. As an illustration, it is shown that the data agree qualitatively with the model proposed by Potanin et al. (J. Chem. Phys. 102 (14) (1995) 5845-5853).     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.     

Study on laminar viscosity and zero shear viscosity of latex systems

The flowing nature and rheological properties of polymethyl methacrylate latex systems in a coaxial cylinder viscometer were studied on the basis of laminar shear flow model and rheological experimental data. The physical meaning of laminar viscosity (eta(i,j)) and zero shear viscosity (eta(0)) were described. We assumed that laminar shear flows depended on position and shear time, so microrheological parameters were the function of position and shear time. eta(i,j) was the viscosity of any shear sheet i between two neighboring laminar shear flows at time t; j was denoted as j=t/Deltat; and Deltat was the interacting time of two particles or two laminar shear flows. tau(i,j) and gamma(i,j) were shear stress and shear rate of any shear sheet i at j moment. According to Newton regulation tau(i,j)=eta(i,j)gamma(i,j), apparent viscosity eta(a) should be a statistically mean value of j shear sheets laminar viscosity at j moment, i.e., eta(a)= summation operator(i=j)eta(i,j)gamma(i,j)/ summation operator(i=j)gamma(i,j). eta(0) was defined as shear viscosity between a laminar shear flow and a still fluid surface, i.e., eta(0)=(tau(i,j)/gamma(i,j))(j-i-->0). These new ideas described above may be helpful in the study of the micromechanisms of latex particle systems and worthy of more research.     

Flow birefringence studies of a concentrated polystyrene solution in a two-roll mill. I. Steady flow and start-up of steady flow

We have studied a 4.8 volume percent solution of a narrow distribution polystyrene with molecular weight 3.84 × 10⁶ in flows generated by a co-rotating two-roll mill. These flows have a stagnation point at the midpoint between the roller axes. Further, they are linear, two-dimensional, and the magnitudes of the strain-rates are greater than the vorticity. The overall objective of our studies is to explore the dynamics of concentrated polymer solutions which are in the highly deformed state that is generated in the two-roll mill. Birefringence data are presented for both steady flow and start-up of steady flow in the two-roll mill. The steady and transient data are used to analyze the linear and nonlinear viscoelastic regions of material behavior. In the nonlinear regime, the birefringence upon start-up shows an initial overshoot followed by a strong undershoot that is enhanced as the ratio of elongation to rotation is increased (i.e., the flow becomes increasingly extensional in character.) We attribute this undershoot, which does not seem to appear in simple shear flows, or flows close to simple shear flow, to polymer segment stretching following an initial period of segment reorientation. Model studies are currently underway to test this notion. © 1992 John Wiley & Sons, Inc.     

Nonlinear rheological behavior of polymer systems for several shear-flow histories

A stiffened and automated Weissenberg rheogoniometer has been used to measure time-dependent nonlinear properties of several polymer solutions in simple shear flow. Departures from finite linear viscoelasticity are correlated with molecular structure. It is shown that certain features of behavior at high shear rates can be explained if the Doi–Edwards equilibration process is taken into account. A method is outlined for calculating the characteristic time τ_e for this process as a function of concentration, molecular weight, temperature, and branch length. This characteristic equilibration time is incorporated into a simplified BKZ constitutive equation. The proposed equation is found to adequately describe a wide range of experimental results both in step-strain and continuous shear flows.     

Effects of Sodium Salicylate on the Microstructure of an Aqueous Micellar Solution and Its Rheological Responses

In this article, we consider the effects of sodium salicylate on the microstructure evolution and rheological responses of an aqueous cetyltrimethylammonium bromide (CTAB) solution. The experimental runs covered CTAB solutions ranging from dilute to semidilute, which were far above its critical micelle concentration. Sodium salicylate (NaSal) was used as a structure-forming agent with the molar ratio of NaSal to CTAB ranging from 0.1 to 10.0. The experimental results showed that the rheological responses of the surfactant solution were influenced strongly by both the CTAB concentration and the molar ratio. At low molar ratios, below 0.3, the surfactant solutions behaved like a Newtonian fluid. However, as the molar ratio increased, the deviation from Newtonian behavior became pronounced. Specifically, for 0.05 M CTAB solutions with molar ratios ranging from 1.0 to 5.0, an apparent yield stress developed at low shear rates and a stress plateau was displayed at intermediate shear rates. When the shear rate exceeded a certain threshold value, the shear stress increased, again passing over the plateau value. In addition, viscoelastic response and relaxation behavior were observed. The relaxation behavior after the cessation of flow was strongly dependent on the molar ratio, which was also confirmed by rheo-optical observations. The optical anisotropy measured by rheo-optical methods was closely related to flow-induced stretching and alignment of the wormy micelles and was consistent with the rheological responses. Copyright 2000 Academic Press.     

The measurement of diffusion and flow in polymer solutions using dynamic NMR microscopy

The new method of dynamic NMR microscopy has been used to obtain velocity and diffusion maps for polymer solutions in capillary flow. In particular we observe power law shear-thinning behaviour in poly(ethylene oxide) (PEO) solutions in the semi-dilute regime but without slip at the walls. Some evidence is apparent for enhanced solvent diffusion along the shear axis in region of high shear.