Wormlike Micellar Solutions Research Articles

Two-species model for nonlinear flow of wormlike micelle solutions. Part I: Model

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

Wormlike Micellar Glycerol Solutions Formed from a Double-Tailed Surfactant with Two Quaternary Ammonium Head Groups.

Herein, a quaternary ammonium surfactant with dual heads and tails, N1,N1,N1,N3,N3-pentamethyl-N3-(3-(2-tetradecylhexadecanamido)propyl)propane-1,3-diaminium dibromide, abbreviated as Di-C14-N2, was synthesized. For the first time, clear observation of aggregate structures formed by surfactants in pure glycerol systems was achieved using cryogenic transmission electron microscopy (cryo-TEM). The system's rheological properties were analyzed using both steady-state shear and oscillatory rheological measurements. The lubricating efficiency of the Di-C14-N2 glycerol solution was assessed for its tribological properties using a tribological wear tester, white light interferometer, and scanning electron microscope. In glycerol, Di-C14-N2 formed long wormlike micelles, which resulted in a glycerol solution with the zero-shear viscosity of 1013 Pa·s at 90 mM, which is the most viscous glycerol system up to now. The system displayed distinct rheological properties from the aqueous system, as evidenced by two intersections in the loss and storage moduli. The formed wormlike micelles in glycerol lead to a significant alteration in the viscoelasticity of the system, thus endowing the Di-C14-N2 glycerol solution with potential as an eco-friendly lubricant. The friction coefficient of the system was found to be 23% lower and the wear rate was 83% lower than that of pure glycerol after the addition of Di-C14-N2. This demonstrates that the addition of Di-C14-N2 greatly improves the frictional properties of pure glycerol. This study offers the possibility of directly observing the aggregate structures formed by surfactants in pure glycerol systems. It contributes to the exploration of the self-assembly behavior of surfactants in nonaqueous polar media, thereby aiding in a deeper understanding of the correlation between molecular structure, mesoscale structure, and macroscopic properties.

Rheo-optics of giant micelles: SALS patterns of cetyltrimethylammonium tosylate solutions in presence of sodium bromide

In this work, we present a systematic study based on Small-Angle Light Scattering (SALS) patterns of the simple shear flow response of semi-diluted solutions of cetyltrimethylammonium tosylate (CTAT; 5.5 wt.% - 0.12 M) in the presence of sodium bromide (NaBr) at different [NaBr]={0,0.12,0.19,0.25,0.3} M concentrations. We evidence a relationship between rheological and light scattering data that reveals a transition into a fast-breaking regime in the dynamics of wormlike micelles formed by the CTAT/NaBr system (Macías et al., 2011; Fierro et al., 2021). This transition into a micellar fast-breaking regime with salt addition ([NaBr]≥0) appears marked by the following features: (i) a decrease in the relaxation time of the material λ0, accompanied by (ii) a decrease of the viscosity level at low shear rates η0 (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003). With these, (iii) the formation of butterfly-like patterns is recorded originating from concentration fluctuations, evolution that is accompanied by: (iv) shear banding in the form of non-monotonic flow curves and (v) slow oscillatory transient responses in start-up flow tests captured theoretically with the Bautista–Manero–Puig (BMP) model. In addition, the Cox–Merz rule is fulfilled at molar salt-to-surfactant ratios of R≥1.5. This results in shorter structure-recovery time-scales than the characteristic-time of the flow (Macías et al., 2011; Fierro et al., 2021; Manero et al., 2002). In the case of the elastic modulus G0, the variation was small, which suggests a transition from an entangled to a multiconnected network, as suggested by Kadoma & van Egmond (1997), Kadoma et al. (1997) and Fierro et al. (2021). From a theoretical perspective, we provide predictions for the shear–stress and the first normal-stress growth coefficients in transient start-up simple shear flow using the BMP model. Here, banding R=1.5 solutions display overshot responses at relatively high shear rates (γ̇=10−30s−1), in-line with experimental findings on the start-up flow of wormlike micellar solutions (Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; Pipe et al., 2010; Mohammadigoushki et al., 2019). Our results are consistent with those reported in other investigations (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003; Kadoma et al., 1997; Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; López-Barrón et al., 2014) and reveal the influence of the Br−-ion used on the mechanical and optical response of the CTAT-NaBr system.

Extensive tip-splitting of injected organic liquid into an aqueous viscoelastic fluid

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele–Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process.

Flow of wormlike micellar solutions over concavities.

We present a comprehensive investigation combining numerical simulations with experimental validation, focusing on the creeping flow behavior of a shear-banding, viscoelastic wormlike micellar (WLM) solution over concavities with various depths (D) and lengths (L). The fluid is modeled using the diffusive Giesekus model, with model parameters set to quantitatively describe the shear rheology of a 100 : 60 mM cetylpyridinium chloride:sodium salicylate aqueous WLM solution used for the experimental validation. We observe a transition from "cavity flow" to "expansion-contraction flow" as the length L exceeds the sum of depth D and channel width W. This transition is manifested by a change of vortical structures within the concavity. For L ≤ D + W, "cavity flow" is characterized by large scale recirculations spanning the concavity length. For L > D + W, the recirculations observed in "expansion-contraction flow" are confined to the salient corners downstream of the expansion plane and upstream of the contraction plane. Using the numerical dataset, we construct phase diagrams in L-D at various fixed Weissenberg numbers Wi, characterizing the transitions and describing the evolution of vortical structures influenced by viscoelastic effects.

Shear layers and plugs in the capillary flow of wormlike micellar gels.

Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex and interesting rheological features. We study the dynamics of these wormlike micellar gels in a pipe-flow scenario using particle imaging and tracking velocimetry and report the existence of plug flows with strong wall slip and non-parabolic velocity profiles for different surfactant concentrations and imposed flow rates. We rationalize these results as features of a developing transient flow of a viscoelastic solution in space and time. We show that evolution of shear layers is governed by intermittent flows, asymmetric velocity profiles and flow induced heterogeneity. Our experiments shed light on the transient fluid dynamics of wormlike micelles in simple geometries and highlight the complexity of flows involving wormlike micellar gels and similar soft matter systems in canonical flows.

Wormlike micellar solutions formed by an anionic surfactant and a cationic surfactant with two head groups.

Innovation in the molecular structure of surfactants is important for the preparation of soft materials with novel properties. In this study, we synthesized a cationic surfactant, N1,N1,N1,N1,N3,N3,N3-pentamethyl-N3-(3-stearamidopropyl)propane-1,3-diammonium bromide, hereafter referred to as C18-DQA. Unlike conventional cationic surfactants, C18-DQA contains two quaternary ammonium head groups and a long-saturated alkyl chain equal to a chain length of 21 carbon atoms. C18-DQA exhibits a low Krafft point of ∼0 °C and a water solubility >1000 mM at 25 °C. The critical micelle concentration (cmc) of C18-DQA was determined to be 0.59 mM using the Nile red method. C18-DQA was mixed with sodium laurate (SL) at different molar ratios to produce transparent solutions with excellent viscoelasticity over a wide concentration range. The 1 : 1.5 molar ratio C18-DQA/SL mixed solutions exhibited gel-like behavior for a total surfactant concentration of 2.88 wt% (75 mM). The solution with a total surfactant concentration of 300 mM (120 mM C18-DQA and 180 mM SL) achieved a maximum zero-shear viscosity (η0) of 4224 Pa s. Cryogenic transmission electron microscopy analysis revealed the formation of extremely long wormlike micelles, with a cross-sectional diameter of 5 nm and contour length >3 μm, in the mixed solutions. C18-DQA and SL molecules were drawn close by electrostatic attractions, leading to a suitable molecular geometry for the extensive growth of wormlike micelles. This work will act as an important reference for the future preparation of highly viscoelastic solutions by mixing cationic and anionic surfactants. The proposed system is also expected to have potential applications in cosmetic formulations, home care products, and oilfield fracturing fluids.

Study of the electroosmotic flow of a structured fluid with a new generalized rheological model

The electroosmotic flow of a viscoelastic fluid in a capillary system was investigated analytically. The rheology of the fluid was characterized by a novel generalized exponential model equation. The charge density obeys the Boltzmann distribution, which governs the electrical double-layer field and body force generated by the applied electrical field. Mathematically, this scenario can be modeled by the Poisson-Boltzmann partial differential equation, by assuming that the zeta potential is small, i.e., less than 25 mV (Debye-Hückel approximation). Considering a pulsating electric field, the shear viscosity and the alteration in the volumetric flow were presented as a function of the material parameters through the characteristic dimensionless numbers by using an exponential-type generalized rheological model. Thixotropy, shear thinning, yield stress mechanisms, and weight concentration were analyzed through numerical results. Finally, the flow properties and rheology were predicted using experimental data reported elsewhere for worm-like micellar solution of cetyl trimethyl ammonium tosilate (CTAT). The rheological equation of state proposed in this study describes the alterations in the structure resulting from applied forces (tangential and normal). These forces induced a structural evolution (kinetic model) due to the relaxation processes caused by shear strain. It is important to mention that in electroosmotic flows, complex behavior such as (i) thixotropy, (ii) rheopexy, and (iii) shear banding flow is scarcely explained in terms of the change in the structure of the fluid under flow.Graphical

Mesoscopic modeling of the effect of branching on the viscoelasticity of entangled wormlike micellar solutions

Mesoscopic modeling of the effect of branching on the viscoelasticity of entangled wormlike micellar solutions

CO2-induced viscoelastic fluids based on a C22-tailed tertiary amine under different pressure and temperature

CO2-switchable viscoelastic surfactant solutions have gained much attention over the last decade; however, large-scale application and the impact of temperature and pressure on such soft colloidal materials have not been explored yet. Here in this work, the impact of environmental parameters including shear rate, pressure, temperature, and salinity on CO2-thickening behavior of aqueous dispersion of N-erucamidopropyl-N,N-dimethylamine (UC22AMPM) was assessed rheologically. Preliminary immiscible water-alternating-CO2 (CO2-WAG) flooding tests with and without UC22AMPM were conducted to highlight the potential of CO2-switchable surfactants in the process of improved oil recovery. The results demonstrated that the dispersion can be viscosified by CO2 15 times higher at 60 °C and 5 MPa, and such thickening power can be switched “on” and “off” upon bubbling and removal of CO2. A universal double-plateau viscosity profile was found as a function of CO2 bubbling time irrespective environmental condition, but the higher the shear rate or the pressure, the shorter the time is needed to reach the plateau viscosity; the higher the temperature, the longer the time is needed to get to the second plateau viscosity. UC22AMPM is first protonated into a long-chain cationic surfactant to form wormlike micellar solution, then the first viscosity plateau; expansion of the viscoelastic solution with CO2 attributes to the second viscosity plateau. Under the simulated oil reservoir of Daqing oilfield, immiscible CO2-WAG flood alone produced an additional 10.5% oil over the initial waterflood recovery, while the addition of 2.1 wt% UC22AMPM in the water slug could recover incremental 5.1% oil relative to pure CO2-WAG. These unique features suggest that coupling injection of CO2 and UC22AMPM dispersion holds great promise for recovering oil during the immiscible CO2-WAG process.

Origin of steady state stress fluctuations in a shear-thinning worm-like micellar system

Large, irregular stress fluctuations under a constant applied shear rate are observed during the flow of dilute worm-like micellar solutions even at low Reynolds numbers. Statistical properties of such fluctuations showing signatures of chaos and elastic turbulence have been studied extensively. Although the mechanisms like boundary slippage, dynamics of shear band interface, time-dependent secondary flows, and inertio-elastic effects are conceived as the possible factors for such striking flow properties, their contributions in different non-linear flow regimes remain poorly understood. Here, we study the Taylor–Couette flow of a well-characterized aqueous worm-like micellar system formed by 2 wt. % cetyltrimethylammonium tosylate and 100 mM sodium chloride (2 wt. % CTAT + 100 mM NaCl). For a fixed applied shear-rate just beyond the onset of shear-thinning, high-speed optical imaging in the flow-gradient plane reveals spatiotemporally varying velocity gradients in the system. In this regime, the magnitude of stress fluctuations remains insignificant. However, the fluctuation becomes substantial beyond a critical shear rate deep inside the non-linear regime of the flow curve when significant free-surface undulations, sustained stick-slip, and elastic recoil events are observed. Imaging in the flow-vorticity and the gradient-vorticity plane indicates that such dynamics are primarily driven by the elasticity-induced turbulent flows in the system. Furthermore, in this regime, we find that the characteristic persistent time of stress fluctuations matches well with the time scales of the stick-slip events, as well as the micellar breaking time, indicating a possible connection between the striking stress dynamics and the micellar kinetics.

Shear banding predictions for wormlike micellar systems under a contraction–expansion complex flow

This study focuses on computational modeling of shear-banded wormlike micellar solutions (WLM) in a complex planar Couette flow, driven by a moving top plate over a rounded-corner 4:1:4 obstruction. The BMP+_τp model is used, which is constructed within an Oldroyd-B-like form, coupled with a thixotropic fluidity-based structure equation. Solute energy dissipation drives fluid–structure adjustment in a construction–destruction dynamics affected by viscoelasticity. This model reproduces conventional WLM features, such as shear thinning, extensional hardening/softening, viscoelasticity, apparent yield stress, and shear banding, with a bounded extensional viscosity and an N1Shear upturn at high deformation rates. The BMP+_τp characterization for shear banding is based on extremely low solvent fractions and appropriate shear-banding intensity parameters. Flow structure is analyzed through velocity, stress, and fluidity, whereupon banded and non-banded response is contrasted at appropriately selected flow rates. Solutions are obtained with our hybrid fe-fv algorithm, capturing essential shear-banded flow features reported experimentally. For a fluid exhibiting banding, banded solutions are generated at a flow rate within the flow curve unstable branch. In the fully developed simple shear flow regions, a split velocity profile is observed, with different viscosity bands at equal stress levels, enhanced with a shock-capture procedure. Non-banded solutions are derived for the lowest and highest flow rates sampled, located in the stable branches. Within the constriction zone, banded profiles are lost due to the mixed non-homogeneous deformation. Shear-banding fluids display less intense viscosity/stress features, correlated with their relatively stronger shear thinning response. The constriction resistance provokes a pressure-level adjustment, leading to fully developed Couette-like constant values upstream–downstream.

Development of a Novel Surfactant-Based Viscoelastic Fluid System as an Alternative Nonpolymeric Fracturing Fluid and Comparative Analysis with Traditional Guar Gum Gel Fluid.

Surfactant-based viscoelastic (SBVE) fluids have recently gained interest from many oil industry researchers due to their polymer-like viscoelastic behaviour and ability to mitigate problems of polymeric fluids by replacing them during various operations. This study investigates an alternative SBVE fluid system for hydraulic fracturing with comparable rheological characteristics to conventional polymeric guar gum fluid. In this study, low and high surfactant concentration SBVE fluid and nanofluid systems were synthesized, optimized, and compared. Cetyltrimethylammonium bromide and counterion inorganic sodium nitrate salt, with and without 1 wt% ZnO nano-dispersion additives, were used; these are entangled wormlike micellar solutions of cationic surfactant. The fluids were divided into the categories of type 1, type 2, type 3, and type 4, and were optimized by comparing the rheological characteristics of different concentration fluids in each category at 25 °C. The authors have reported recently that ZnO NPs can improve the rheological characteristics of fluids with a low surfactant concentration of 0.1 M cetyltrimethylammonium bromide by proposing fluids and nanofluids of type 1 and type 2. In addition, conventional polymeric guar gum gel fluid is prepared in this study and analyzed for its rheological characteristics. The rheology of all SBVE fluids and the guar gum fluid was analyzed using a rotational rheometer at varying shear rate conditions from 0.1 to 500 s-1 under 25 °C, 35 °C, 45 °C, 55 °C, 65 °C, and 75 °C temperature conditions. The comparative analysis section compares the rheology of the optimal SBVE fluids and nanofluids in each category to the rheology of polymeric guar gum fluid for the entire range of shear rates and temperature conditions. The type 3 optimum fluid with high surfactant concentration of 0.2 M cetyltrimethylammonium bromide and 1.2 M sodium nitrate was the best of all the optimum fluids and nanofluids. This fluid shows comparative rheology to guar gum fluid even at elevated shear rate and temperature conditions. The comparison of average viscosity values under a different group of shear rate conditions suggests that the overall optimum SBVE fluid prepared in this study is a potential nonpolymeric viscoelastic fluid candidate for hydraulic fracturing operation that could replace polymeric guar gum fluids.

Numerical Study on the Unstable Flow Dynamics of Wormlike Micellar Solutions past a Sphere in the Creeping Flow Regime.

The flow dynamics of wormlike micellar solutions around a sphere is a fundamental problem in particle-laden complex fluids but is still understood insufficiently. In this study, the flows of the wormlike micellar solution past a sphere in the creeping flow regime are investigated numerically with the two species, micelles scission/reforming, Vasquez-Cook-McKinley (VCM) and the single-species Giesekus constitutive equations. The two constitutive models both exhibit the shear thinning and the extension hardening rheological properties. There exists a region with a high velocity that exceeds the main stream velocity in the wake of the sphere, forming a stretched wake with a large velocity gradient, when the fluids flow past a sphere at very low Reynolds numbers. We found a quasi-periodic fluctuation of the velocity with the time in the wake of the sphere using the Giesekus model, which shows a qualitative similarity with the results found in present and previous numerical simulations with the VCM model. The results indicate that it is the elasticity of the fluid that causes the flow instability at low Reynolds numbers, and the increase in the elasticity enhances the chaos of the velocity fluctuation. This elastic-induced instability might be the reason for the oscillating falling behaviors of a sphere in wormlike micellar solutions in prior experiments.

On the startup behavior of wormlike micellar networks: The effect of different salts bound to the same surfactant molecule

We report on shear startup data for two wormlike micellar solutions, differing only in concentration and type of two binding aromatic sodium salts. The surfactant molecule is cetylpiridinium chloride at a fixed concentration (100 mM). Sodium salicylate (NaSal) and diclofenac sodium (Diclo) are used as binding salts at concentrations 68 mM NaSal and 52 mM Diclo such that both systems are fully entangled and their linear viscoelastic response is essentially identical. Both systems show the linear response typical of a wormlike micellar solution, with terminal behavior at low frequencies, a well-defined moduli crossover, and a plateau modulus. In the nonlinear regime, however, the behavior of the two systems is totally different, suggesting that the molecular structure difference of the salts and their binding activity to the surfactant molecule are both crucial to determine the fast flow behavior. The NaSal solution shows a very complex rheological response, with strain hardening and very sharp stress peaks, whereas the solution containing Diclo behaves much like ordinary linear polymers, exhibiting pronounced overshoots as well as moderate undershoots in the transient shear viscosity, before approaching the steady state. This polymerlike behavior has also been proved by successfully comparing data with predictions of a constitutive equation recently adopted for both entangled polymers and linear wormlike micelles. As far as NaSal is concerned, a phenomenological model based on rubber network theory is developed, which describes the flow singularities. A physical interpretation of the different behavior in the nonlinear regime is also suggested.

Prediction of the Viscoelastic Properties of a Cetyl Pyridinium Chloride/Sodium Salicylate Micellar Solution: (II) Prediction of the Step Rate Experiments.

The reliable viscoelastic characterization and prediction of micellar solution is still required in industrial applications of the solution, e.g., in surfactant flooding and pharmaceuticals. Based on the recent theoretical characterization of the viscoelastic properties of a cetyl pyridinium chloride/sodium salicylate (CPyCl/NaSal) wormlike micellar solution with a structuralized constitutive model in the work published in 2022, the present work predicted five groups of transient shear viscoelasticities of the solution experimentally obtained in 2010, which include the first normal stress difference (N1) versus time curve in the start-up experiment, the shear stress (τ12) in the start-up experiment, τ12 in the long-term start-up experiment, the stress relaxation upon cessation of steady shear flow, and the transient N1/τ12 in the step strain experiment. The study findings clearly show an improvement in the predictions of the viscoelastic properties of the micellar solution compared with those predicted previously. For example, the experimental N1/τ12 is 9 at the strain of 9 in the step strain experiment, and the corresponding previous and present predictions are 2.47 and 8.45, respectively.

Role of micellar entanglements on kinetics of shear banding flow formation

We investigate the effects of micellar entanglement number on the kinetics of shear banding flow formation in a Taylor–Couette flow. Three sets of wormlike micellar solutions, each set with a similar fluid elasticity and zero-shear-rate viscosity, but with varying entanglement densities, are studied under the startup of steady shear. Our experiments indicate that in the set with low fluid elasticity, the transient shear banding flow is characterized by the formation of a transient flow reversal in a range of entanglement densities. Outside of this range, the transient flow reversal is not observed. For the sets of medium and high elasticities, the transient flow reversals exist for relatively small entanglement densities and disappear for large entanglement densities. Our analysis shows that wall slip and elastic instabilities do not affect the transient flow feature. We identify a correlation between micellar entanglement number, the width of the stress plateau, and the extent of the transient flow reversal. As the micellar entanglement number increases, the width of the stress plateau first increases; then, at a higher micellar entanglement number, the plateau width decreases. Therefore, we hypothesize that the transient flow reversal is connected to the micellar entanglement number through the width of the stress plateau.

Flow past a sphere: Numerical predictions of thixo-viscoelastoplastic wormlike micellar solutions

In this work, we present numerical solutions to the benchmark flow past a sphere problem considering the rheology of semi-diluted and concentrated wormlike micellar viscoelastic solutions using the most recent model-variant of the Bautista–Manero–Puig (BMP) family of fluids, i.e. the BMP+ _ τ p model (López-Aguilar et al., [1] ). This study is performed using our in-house finite volume/element algorithm, stabilised to attain highly-elastic non-linear solutions with two novel constitutive and boundary-condition implementations, i.e. the ABS- f (ABSolute f -functional) and the VGR (Velocity GRadient) corrections (López-Aguilar et al., [2] ). The structuring level of various wormlike micellar fluids with different solute concentrations (from semi-diluted to extremely concentrated solutions) and degrees of strain-hardening is studied with a dynamic dimensionless fluidity that connects the internal structure construction-destruction dynamics with viscoelasticity. In complex flow, a viscoelastic flow-regime unveils the prediction of a flow transition from a stable steady flow (related to a steady sphere settling) to an unsteady quasi-periodic flow regime, in which transient cycles of vortex formation-disappearance behind the sphere are present, resembling experimental findings on negative-wake instabilities and oscillations in the settling velocity for the descend of particles in wormlike micellar solutions. This instability is predicted here for semi-diluted to concentrated wormlike micellar solutions and it is located in flow-rate ranges corresponding to extensional Deborah numbers in the interval of around 26 . 7 ≤ D e e x t ≤ 40 . 3 , as reported experimentally. This behaviour is correlated with a chaotic flow-structure behind the obstacle, for which strong fluctuation in the fluid’s internal-structure is recorded. In the steady viscoelastic flow regime, correlation between the BMP+ _ τ p fluidity structure-variable and its normal-stress response around and downstream of the sphere (in the form of localised extrema) is detected, where interaction between the rheological response of the material and mixed shear-to-extensional deformation provide insights into the forces the fluid elements experiment in the sphere wake. Here, a monotonic decline in the drag-correction factor is observed, this being one of the main experimental manifestations of the steady sphere-settling phase in these materials. These findings may serve to further understand flow transitions and instabilities related to negative wakes in this kind of shear-thinning extensional-hardening fluids (Rothstein and Mohammadigoushki, [3] ). In a plastic regime, complex thixo-viscoelastoplastic BMP+ _ τ p features manifest through the prediction of fore-aft asymmetries promoted by the thixotropic structure construction-destruction and viscoelastic properties of the model under extremely low solute-concentrations. Predicted yield-fronts resemble those reported experimentally by Holenberg et al. [4] for carbopol solutions. • Negative-wake instability predictions in the De -range recorded experimentally. • Correlation between extensional viscosity and normal stresses in the sphere wake. • Localised N 1 and internal-structure f -functional in the sphere wake. • First normal-stress activity in the sphere wake follows extensional viscosity response. • Asymmetric yield-fronts under highly-concentrated gel-like wormlike micellar solutions.

A Novel ZnO Nanoparticles Enhanced Surfactant Based Viscoelastic Fluid Systems for Fracturing under High Temperature and High Shear Rate Conditions: Synthesis, Rheometric Analysis, and Fluid Model Derivation.

Surfactant-based viscoelastic (SBVE) fluids are innovative nonpolymeric non-newtonian fluid compositions that have recently gained much attention from the oil industry. SBVE can replace traditional polymeric fracturing fluid composition by mitigating problems arising during and after hydraulic fracturing operations are performed. In this study, SBVE fluid systems which are entangled with worm-like micellar solutions of cationic surfactant: cetrimonium bromide or CTAB and counterion inorganic sodium nitrate salt are synthesized. The salt reagent concentration is optimized by comparing the rheological characteristics of different concentration fluids at 25 °C. The study aims to mitigate the primary issue concerning these SBVE fluids: significant drop in viscosity at high temperature and high shear rate (HTHS) conditions. Hence, the authors synthesized a modified viscoelastic fluid system using ZnO nanoparticle (NPs) additives with a hypothesis of getting fluids with improved rheology. The rheology of optimum fluids of both categories: with (0.6 M NaNO3 concentration fluid) and without (0.8 M NaNO3 concentration fluid) ZnO NPs additives were compared for a range of shear rates from 1 to 500 Sec−1 at different temperatures from 25 °C to 75 °C to visualize modifications in viscosity values after the addition of NPs additives. The rheology in terms of viscosity was higher for the fluid with 1% dispersed ZnO NPs additives at all temperatures for the entire range of shear rate values. Additionally, rheological correlation function models were derived for the synthesized fluids using statistical analysis methods. Subsequently, Herschel–Bulkley models were developed for optimum fluids depending on rheological correlation models. In the last section of the study, the pressure-drop estimation method is described using given group equations for laminar flow in a pipe depending on Herschel–Bulkley-model parameters have been identified for optimum fluids are consistency, flow index and yield stress values.

Evaluation of constitutive models for shear-banding wormlike micellar solutions in simple and complex flows

Wormlike micellar solutions possess complex rheology: when exposed to a flow field, the wormlike micelles may orientate, stretch, and break into smaller micelles. Entangled wormlike micellar solutions exhibit shear banding characteristics: macroscopic bands with different local viscosities are organized and stacked along the velocity gradient direction, leading to a non-monotonic flow curve in simple shear. We present a systematic analysis of four commonly used constitutive models that can predict a non-monotonic flow curve and potentially describe the rheology of entangled wormlike micellar solutions with shear-banding characteristics: the Johnson–Segalman, the Giesekus, the thixotropic viscoelastic, and the Vasquez–Cook–McKinley (VCM) models. All four constitutive models contain a stress diffusion term, to account for a smooth transition between the shear bands and ensure a uniqueness of the numerical solution. Initially, the models are fitted to shear and extensional experimental data of a shear-banding wormlike micellar solution. Subsequently, they are employed to solve three non-homogeneous flows: the Poiseuille flow in a planar channel, the flow in a cross-slot geometry, and the flow past a cylinder in a straight channel. Each of these flows exposes the wormlike micellar solution to different flow kinematics (shear, extensional, and mixed), revealing different aspects of its rheological response. The predictive capability of each model is evaluated by directly comparing the numerical results to previously published experimental data obtained from microfluidic devices with corresponding flow configurations. While all the models can describe qualitatively the characteristic features observed experimentally in the benchmark flows, such as plug-like velocity profiles and elastic instabilities, none of them yields a quantitative agreement. Based on the overall performance of the models and also accounting for their differing numerical complexity, we conclude that the Giesekus model is at present the most suitable constitutive equation for simulating shear banding wormlike micellar solutions in flows that exhibit both shear and extensional deformations. However, the quantitative mismatch between model predictions and experiments with wormlike micellar solutions demand that improved constitutive models be developed in future works. • Comparison of popular constitutive models for wormlike micellar solutions. • Evaluation of their performance in rheometric and inhomogeneous shear flows. • Investigation of their predictions in extensional flows and elastic instabilities. • The models can only make qualitative predictions.