Flow-induced structures observed in a viscoelastic reverse wormlike micellar system by magnetic resonance imaging and NMR velocimetry

Abstract

The aim of the present work is to illustrate and discuss an application of rheo-NMR techniques in the investigation of the flow micro-morphology of a rheo-thinning fluid. The viscoelastic material is composed by weakly hydrated nonionic Wormlike Micelles (WM), stabilized by the biocompatible phospholipid in an organic solvent (lecithin organogel). By applying rheo-NMR techniques, such as micro-imaging and flow velocimetry in Couette flow, to lecithin organogels in the concentrated isotropic phase, a new phase nucleating inhomogeneously at the inner rotating cylinder showing periodic fluctuations in space in some cases, has been identified for applied shear rates within the isotropic-nematic stress plateau. On the other hand, evident slippage phenomena have been found in flow regimes consistent with a full shear-induced nematic state. Bulk rheometric investigations executed in oscillatory, steady state and transient mode have been finally carried out to bridge different flow micro-heterogeneities detected by rheo-NMR with a variety of mechanical responses manifested by lecithin WM.

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Introduction

Wormlike Micelles (WM) are one of many self-assembled micellar morphologies spontaneously formed by most classes of amphiphilic surfactant, whether ionic, zwitterionic or nonionic ones.^1,2 Above a threshold surfactant volume fraction ϕ*, WM entangle forming physical networks whose topology and dynamics can range from unbranched living polymers to interconnected living networks.^3–6 Here, the term “living” is referred to the transient nature of WM, whose chain connectivity is achieved through non-covalent bonding and is subjected to breaking and recombination events. WM can be long even several μm and are polydisperse in size, the equilibrium distribution being determined by the interplay between the entropy and the film curvature energy.⁷

Furthermore, once WM are subjected to a shear flow they manifest peculiar dynamical and rheological properties, which have been recently overviewed in several excellent books and reviews.^8–13 One of the most fascinating phenomena displayed by WM solutions under shear flow is that of shear-banding in which two or more distinct spatial regions sustain different local strain rates, despite nominally maintaining a uniform stress.¹⁴ This stress plateau, which is a region of flow curve observed experimentally when the velocity gradient [small gamma, Greek, dot above] exceeds a critical shear rate [small gamma, Greek, dot above]*, is inherently unstable and leads to coexistence of flow of material following separate stress branches, in a proportion satisfying the overall rate of strain condition.⁹ Shear banding in the stress plateau region of many WM systems has been convincingly demonstrated by different techniques such as NMR velocimetry,^15,16 Laser Doppler Velocimetry (LDV),¹⁷ dynamic light scattering¹⁸ and ultrasonic velocimetry.¹⁹ In particular, the latter technique, which is based on the acquisition of ultrasonic speckle signals formed by interferences of the backscattered echoes from incident pulses, is an efficient, cost-effective tool to measure time-resolved velocity profiles in a large range of fluids.²⁰

In systems at even high WM concentrations close to the isotropic-to-nematic (I–N) phase transition, shear banding has been identified in terms of coexisting states of different directional order, wall slip, and shear stress fluctuations,²¹ as suggested by birefringence,^22,23 NMR spectroscopy²⁴ and small angle neutron scattering (SANS).²⁵ This phenomenon has been also observed in vesicular systems and attributed to lamellar and multilamellar vesicle coexistence.²⁶ Careful experimental observations in entangled micellar solutions as well as recent calculations show that the dynamical response of these bands can be very complex with the shear-banded fluid region exhibiting traveling internal waves or even chaotic fluctuations in the measured stress.^27,28 A wide range of WM systems requires the presence of a cosurfactant or counter-ion: canonical examples are the surfactant micellar systems CTAB/NaNO₃ (cetyltrimethylammonium bromide) in water^29–32 and CPyCl/NaSal (cetylpyridinium chloride/sodium salicylate) in water.^33,34

However, less attention has been given to the rheological response of oil continuous WM systems, where instead the head-groups are shielded from the oil and offer the advantage to neglect the electrostatic interaction played by salt concentration. In particular, no micro-images nor velocity profiles have been reported for reverse WM under shear flow, at the best of our knowledge.

To fill this gap, we present a viscoelastic fluid formulated with the zwitterionic surfactant lecithin (phosphatidyl-choline), a natural phospholipid that accounts for more than 50% of the lipid matrix of biological membranes,³⁵ which is able to form reverse (water-in-oil) WM,^36,37 depending on the type of organic solvent used as continuous phase.^5,38–41

Previous studies demonstrated that lecithin reverse micelles in cyclohexane are spherical at very low micellar (surfactant plus water) volume fraction ϕ, but undergo uniaxial water-induced elongation to become polydisperse wormlike aggregates with lengths from several hundred nm to μm as ϕ and W₀, the water-to-surfactant mole ratio, are increased.^42,43 Once a threshold micellar volume fraction ϕ* (which depends on W₀) has been reached, these inverted WM start to entangle and form a transient network, similar to semidilute polymer solutions, and they form highly viscous and non-Newtonian solutions at even moderate concentrations. At still higher concentrations, liquid crystalline mesophases exhibiting nematic, hexagonal, or lamellar ordering have been found.⁴⁴

These so-called lecithin organogels are characterized by considerably high viscosities (10–10⁵ Pa s), depending on ϕ and W₀, with a maximum in correspondence of a characteristic W₀-value (solvent dependent).^36,45 Anhydrous lecithin WM have been also obtained in cyclohexane and n-decane by substituting water with sodium deoxycholate in trace amounts.⁴⁶ The dynamics of reverse WM formed by lecithin in pure cyclohexane have been the subject of several studies. Recent results coming from conventional rheology,³⁸ micro-rheology through diffusive wave spectroscopy,⁴⁷ rheo-SANS,^48,49 rheo-NMR⁵⁰ and rheology combined with NMR self-diffusion experiments⁵¹ indicate that the lifetime of lecithin WM organogel in cyclohexane is unusually long such that they can be considered almost equivalent to true polymer solutions in a time window of order of minutes. Anomalous molecular diffusion phenomena observed in lecithin–water–cyclohexane reverse micellar system, have been illustrated and quantitatively described in Angelico et al.⁵² It has been also shown that lecithin WM are transiently capable of transmitting elastic waves over macroscopic distances.⁵³

According to this scenario, dynamic rheology of lecithin organogels made of oil phase rich in cyclohexane is consistent with the typical rheological response ascribed to real polydisperse polymer solutions. Extensive experimental research has been reported on organogels based on lecithin from soybean and egg sources and on biocompatible oils, indicating they are particularly suited as delivery vehicles for widespread functional molecules.^54–56

The aim of this article is to advance our understanding on the earlier issues by an experimental characterization of the complex shear flow in this model micellar system. Rheo-NMR combines rheology and nuclear magnetic resonance (NMR) methods. Therefore, we have used NMR micro-imaging and NMR velocimetry to provide the first flow visualization measured in a reverse wormlike micellar system across the gap of a Couette shear cell. Such results have been integrated with conventional rheometric data to gain further details about the dynamics of these organogels with strong polymer-like properties.

Experimentals

Materials

Soybean lecithin, Epikuron 200, with a purity of 95% and an average molecular weight of 772 Da, was a kind gift from Degussa AG, Germany and was used as received. For the density of lecithin, a value of 1.0198 kg L⁻¹ was considered.⁵⁷ Cyclohexane purity >99% was obtained from Fluka Chemie AG. Water was Millipore filtered.

Sample preparation

Selected micellar volume fractions (lecithin + water) of, respectively, ϕ = 7 and 14% were obtained by dilution, adding weighed quantities of cyclohexane to a stock organogel with ϕ = 28% and fixed water-to-lecithin molar ratio W₀ = 10. All samples were let to equilibrate until the obtained materials were found stable and optically transparent, (2–3 days). For W₀ = 10, the system forms an isotropic phase (I), where reverse WM are highly entangled in a transient network, up to approximately ϕ = 33%, followed by a nematic phase (N) stable up to ϕ = 45%.^44,50 Temperature was everywhere fixed at 289 K.

Rotational rheometry

Shear startup measurements were performed using a RFS-II Reometrics strain controlled rheometer equipped with a bob-and-cup flow geometry with an inner radius of 16 mm and a gap of 1 mm. This setup allowed accurate transient controlled-strain-rate experiments. Direct measurements of stress relaxation following cessation of steady shear were thus made possible, especially at short times. Dynamic oscillatory rheology investigations were performed in triplicate using the stress controlled rheometer MARS III Thermo Haake Scientific equipped with a cone–plate geometry and cone–plate angle 1° (gap 53 μm) with diameter 20 mm. To prevent evaporation of cyclohexane, the cone–plate cell was covered by a solvent trap. The temperature was kept constant at 289 K. Both the stress and strain sweep oscillations were first carried out at a constant frequency of 1 Hz in order to determine the linear viscoelastic region. Once this was determined, isothermal frequency sweep experiments were carried out in the range 1 × 10⁻³ ≤ ω ≤ 500 rad s⁻¹ to study the frequency-dependent behavior of complex viscosity η*, storage G′ and loss G′′ moduli.

NMR micro-imaging

A Bruker NMR spectrometer AVANCE 300 Wide Bore equipped with microscopic imaging capabilities was used to acquire the ¹H images. Rheological cell Couette was centered inside the 25 mm diameter coil of a Bruker imaging probe and the water signal was set on resonance (ca. 300 MHz). The proton signal was processed and reconstructed by an image processing software (Paravision, Bruker Analytische Messtechnik GmbH, Germany). A flow device was driven by a shaft sitting in the magnet bore, which was turned by a stepper-motor gearbox assembly mounted above the magnet bore. An airflow regulator, yielding a temperature stability of ±0.1 °C, controlled the temperature at the external surface of the cup. Under shear, the temperature of the sample remained fixed at 289 ± 0.4 K. Gradient Echo Fast Imaging (GEFI) was used to determine the proton-density weighted images and optimal position of selected 1 mm thick two-dimensional slices. Sinc-3 pulses (attenuation 23 dB, length 1 ms) were used for both the excitation and refocusing pulses. The field of view was fixed at 16 mm × 16 mm and a matrix size of 128 × 128 was used, producing image voxel dimensions of 0.125 × 0.125 × 1 mm (voxel volume = 0.0156 mm³). Acquisition, repetition and echo times for GEFI pulse sequence corresponded to 7 s, 140 ms and 1.9 ms, respectively. Finally, acquired proton-density weighed images were elaborated with Bruker software. The inner rotor was loaded with internal liquid reference composed by the mixture H₂O (60%) + D₂O (40%). Details about the NMR tool used to perform imaging experiments can be found in Coppola et al.⁵⁸ who applied for the first time the MRI technique to study the flow dynamics of lecithin organogels.

NMR velocimetry

The velocity profiles were obtained by using a SEVI NMR (Spin Echo Velocity Image) velocimetry pulse sequence as a two- and three-dimensional method, where two dimensions contain spatial information and the third, or the image, detects spins displacement during an observation time Δ. This information was used to calculate the velocity vectors and the dispersion at each position in 2D spatially resolved slices. The field of view was 10 × 40 mm with matrix 128 × 128 pixels. In this study, a cylindrical Couette cell was used with bob diameter 17 mm and gap 1 mm. The inner cylinder of the cell was rotated continuously at an imposed shear rate [small gamma, Greek, dot above] = 10 s⁻¹ to the fluid at rest. The velocity profile was mediated over a period of 44 min in which the shear flow was continuously applied, corresponding also to the acquisition time for SEVI data set. The central part of the rotor was filled with the mixture H₂O (60%) + D₂O (40%) as reference fluid; the motor was run up in rate-controlled mode. Further details on the NMR velocimetry technique can be found in Callaghan et al.⁵⁹

Results and discussion

Dynamic rheology

Fig. 1 shows the log–log plot of the complex viscosity η*, storage G′ and loss G′′ moduli obtained from oscillatory shear frequency sweep tests at a low strain (2%) at 289 K. For simplicity, rheological data have been reported for the micellar volume fractions ϕ = 7 and 28%. It is evident that both G′ and G′′ are slightly upwardly sloping and a “true” rubber plateau G₀ in G′ seems to be approximately reached for ω → ∞ while the crossover frequencies (G′ ≈ G′′) can be identified at 0.067 and 2 × 10⁻³ rad s⁻¹, for ϕ = 7 and 28%, respectively.

Fig. 1 Storage G′ and loss G′′ moduli (left axis) and complex viscosity η* (right axis) vs. frequency ω for organogel micellar volume fractions (lecithin + water) ϕ = 7% (red-coloured symbols) and ϕ = 28% (blue-coloured symbols). Solid lines are power law fits to viscosity data with slopes – 0.7 (red, 7%) and – 0.9 (blue, 28%), respectively.

Their reciprocal value provides a rough estimate of the respective dominant relaxation times.⁶⁰

The deviation from the theoretical predictions of the Maxwell model⁶¹ for equilibrium polymer can be checked by plotting G′′ versus G′ in the so called Cole–Cole plot, where the behaviour observed for ϕ = 7, 14 and 28% samples are compared all together (Fig. 2).

Fig. 2 Oscillatory rheology data G′′ vs. G′ illustrated as Cole–Cole plot at different volume fractions ϕ = 7, 14 and 28%. For WM solutions described by a Maxwellian behavior, the Cole–Cole plot should follow a perfect semi-circle, likewise the one displayed in the inset partially overlapping data of the most diluted sample.

For a single Maxwell element, such representation should result in a perfectly semi-circular shape with a diameter equal to the plateau modulus G₀.

Basically, deviations from the semi-circular prevision indicate a departure from ideal Maxwell behaviour evidencing a system characterized by multi-relaxation times.⁶²

The more concentrated organogel shows a slight dip in G′′ followed by a turn up, which may indicate a crossover to a regime where the dominant motion is not reptation but other mechanisms such as ‘breathing’ and Rouse motion.⁶³

Steady state rheology

Taking the steady-state value of the shear stress σ acquired during step rate experiments, we can plot the flow curves in Fig. 3 where a characteristic stress plateau is clearly observed for all the samples, in accord with the literature.⁶⁴

Fig. 3 Flow rheograms acquired at 289 K for lecithin organogel samples at various volume fractions ϕ = 7–28%.

Rheological investigations carried out below [small gamma, Greek, dot above] = 0.01 s⁻¹ can be found in previous works.^39,53

The high shear rate branch signs the limits of the stress plateaus: [small gamma, Greek, dot above] ≈ 0.5 s⁻¹ for ϕ = 7–14% and [small gamma, Greek, dot above] ≈ 0.7 s⁻¹ for ϕ = 28%. For the latter composition, at higher shear rates such as 10 s⁻¹, rheo-SANS studies demonstrated the occurrence of an aligned state in the flow direction, identified as a shear-induced nematic phase.⁴⁹ Furthermore, within the stress plateau region where nematic (weakly oriented WM) and isotropic phases coexist, rheo-SANS measurements acquired in the vorticity–velocity plane revealed out-of-plane oscillations of the nematic order parameter.⁵³

Those findings could be attributable to the onset of flow instabilities such as, e.g., Taylor-like vortices, as it will be suggested by direct flow visualization with NMR imaging (vide infra).

Transient rheology

During transient step rate experiments, a classical elastic overshoot was observed to occur at critical strain γ* for applied shear rates within the stress plateau. The numerical value of γ* was found depending only on the sample volume fraction: γ* ≈ 8, 4 and 2 identified for ϕ = 7, 14 and 28%, respectively. The critical strain has been previously interpreted in terms of micellar network fracture.³⁹ For unbreakable polymer chains, the Doi–Edwards tube model predicted that a maximum overshoot in the shear stress should occur at a total strain γ = [small gamma, Greek, dot above]t value of 2.⁶⁵ Fig. 4 collects several step rate runs carried out in CR (Control Rate) mode for sample ϕ = 7% where the position of the overshoot maxima can be identified at γ* ≈ 8 independently of imposed shear rate. Then, “interrupted” step strain experiments were run in CR mode followed by shear stress relaxation.

Fig. 4 Step rate runs carried out in CR (Control Rate) mode for sample ϕ = 7% where the position of the overshoot maxima can be identified at γ* ≈ 8 independently of imposed shear rate.

Fig. 5 shows an example of this test carried out for the sample ϕ = 7% where the measured shear stress has been plotted vs. the accumulated strain γ = [small gamma, Greek, dot above]t. Transient experiments have been carried out as follows: first, a ramp of controlled strain rate [small gamma, Greek, dot above] = 0.043 s⁻¹ chosen within the stress plateau, was imposed at time t = zero and the shear stress response σ was initially monitored for t = 10 s.

Fig. 5 Semilogarithmic plot of step rate runs acquired in control rate mode at imposed strain rate [small gamma, Greek, dot above] = 0.043 s⁻¹ for lecithin organogel ϕ = 7%. The stress response σ was measured during each signed shearing time; then the shear was stopped at t = 10, 20, 40 and 80 s before the overshoot and 1200 s well beyond the overshoot and the correspondent stress relaxation σ_R was recorded for 30 min until the full relaxation had been reached. For clarity, stress was plotted as a function of strain both during the shear and afterwards (post-ramp period). The inset illustrates an example of a biexponential fit of the normalized stress relaxation, σ′_R = σ_R(t)/σ(0)_{shear off} exhibiting a 2-step decay after flow cessation (t shearing = 80 s).

Then, the strain was switched off and the correspondent stress relaxation σ_R was recorded for 30 min until the full relaxation had been reached. For clarity, σ was plotted vs. γ for the data collected during both strain ramp and post-ramp, although the latter part of each experiment should be represented more correctly as a function of time. Afterword, the sequence was repeated using the same sample in the cell, by increasing the shearing time for t = 20, 40 and 80 s, respectively. The last experiment of the series was performed by applying the same shear rate of [small gamma, Greek, dot above] = 0.043 s⁻¹ for t = 1200 s until steady state was reached, followed by the measurement of stress relaxation σ_R.

For imposed values of deformations less than the critical strain γ* correspondent to the position of the overshoot, the stresses at shear-off nicely belonged to the same curve obtained for the longest strain sweep (t = 1200 s), demonstrating no shear history effect and indicating that elastic energy totally dissipated before reaching the overshoot. After shear off, the relative stress relaxation σ′_R = σ_R(t)/σ(0)_{shear off} followed a two-step decay process (see the inset in Fig. 5), as a sum of exponential functions: σ′_R = b exp(−t/τ_f) + (1 − b)exp(−t/τ_s) where the fast and slow time constants τ_f and τ_s may be obtained from the best non-linear fits to the above equation, as well as the relative weight b. For γ < γ* it can be envisaged that WM are both stretched and oriented by the imposed flow. Therefore, following shear cessation, the fast component could be ascribed to the relaxation of chain stretch (Rouse relaxation time) before reptation has appreciably reoriented the chains and the slow one to the time required for a chain to fully recover its equilibrium entanglement density (tube disengagement time).^14,66

From the main plot of Fig. 5 it was indeed evident that the initial part of stress relaxation σ_R collected just after the arrows, shrank with increasing the applied strain amplitude γ, thus suggesting that the initial re-entanglement rate was faster at high shear strains. The magnitude of chain stretch increases with the step strain amplitude, leading to steeper drop in σ_R once the imposed γ has been stopped and, therefore, to an increasing of the fast relaxation time component.⁶⁷ Similar bi-exponential relaxation processes recorded at shear-off for γ < γ* were observed also at higher lecithin organogel volume fractions.

NMR micro-imaging of the interface

From the perspective of conjoining magnetic resonance and rheology, the field known as rheo-NMR facilitates progress towards understanding the mechanical properties of materials by correlating the controlled deformation of the sample with experimentally observed local strain rate (velocimetry) over the entire volume (imaging).⁶⁸ Details about the rheo-NMR theory can be found in Callaghan.^69,70

Therefore, we have performed rheo-¹H-NMR experiments using a cylindrical Taylor–Couette cell in which the solution in the annulus (gap 1 mm) was imaged in order to investigate spatially dependent NMR parameters. Fig. 6 gathers several patterns acquired at three different shearing times in the low shear regime [small gamma, Greek, dot above] = 0.036 s⁻¹ along the coexistence plateau in steady state conditions for the most concentrated sample ϕ = 28%, which we recall to be near the equilibrium liquid-nematic two-phase region.⁴⁴ The grey levels visualize the interface in the gap, dark grey and light grey regions being associated, respectively, with the minima and maxima of the interface amplitude viewed from the inner cylinder.

Fig. 6 Two-dimensional slices ¹H-NMR GEFI images recorded for lecithin organogel ϕ = 28% at T = 289 K. The rotor is loaded with internal liquid reference, H₂O (60%) + D₂O (40%) shown as dark grey and evidenced by blue lines, the vial result to be upside down; the sample in the gap is evidenced by red lines. The liquid between the reference and the sample is a small amount of sample leaked from the Couette. Vertical z and horizontal r yellow arrows indicate the vorticity (neutral) and velocity gradient directions, respectively, of the Taylor–Couette cell with gap 1 mm. The upper part of the collected images results to be bended due to the end of the coils generating an artifact. Conditions: applied shear rate = 0.036 s⁻¹. (A) Images acquired after t = 5 min (B) t = 65 min and (C) t = 155 min. Shearing times were also converted into strain units γ.

A new phase nucleating inhomogeneously at the inner wall of the Couette cell along the vorticity direction in coexistence with the isotropic phase can be easily identified already after 5 min (γ = 10.8), which persist at even longer shearing times.

Remember that the position of stress overshoot for this sample is reached for γ* ≈ 2, independently of [small gamma, Greek, dot above]. The appearance and coarsening of bright and dark bands at the vicinity of the inner rotating cylinder have been identified also for other selected values of applied [small gamma, Greek, dot above] within the stress plateau such as [small gamma, Greek, dot above] = 0.028–0.043 s⁻¹ (Fig. 7) and [small gamma, Greek, dot above] = 0.07–0.14 s⁻¹ (Fig. 8).

Fig. 7 Two-dimensional grayscale ¹H-NMR GEFI images acquired for lecithin organogel ϕ = 0.28 at T = 289 K. Interface patterns in steady state for applied [small gamma, Greek, dot above] = 0.043 s⁻¹ after (A) t = 35 min (γ = 90.3) and (B) t = 85 min (γ = 219.3). (C) Axial profiles (width = 15 mm) selected in the cell gap where the ¹H-NMR signal intensity is averaged at rest (left) and from t = 5 min to t = 155 min at [small gamma, Greek, dot above] = 0.028 s⁻¹ (middle) and [small gamma, Greek, dot above] = 0.043 s⁻¹ (right) for comparison. (D) FT of ¹H-NMR intensity averaged in the selected profiles as a function of the spatial frequency.

Fourier modes for the spatial modulation along the vorticity axis have been also calculated from the ¹H-NMR intensity averaged in the selected profiles and displayed in Fig. 7D and 8D, respectively. Fourier analyses indicate that the perturbed flow consists of a vortex-type pattern with wavelength 2π/k, k being 3 and 4 mm⁻¹, respectively, for [small gamma, Greek, dot above] = 0.028 s⁻¹ (Fig. 7D) and [small gamma, Greek, dot above] = 0.07 s⁻¹ (Fig. 8D). The occurrence of elastic instabilities, generally observed in polymer solutions, may be responsible for the nucleation of Taylor-like vortices, developing along the neutral axis with a characteristic length-space frequency. In particular, a second peak near 10 mm⁻¹ has been also identified (for [small gamma, Greek, dot above] = 0.028 s⁻¹ in Fig. 7D), the origin of which could be likely related to artefacts arising from a secondary viscoelastic flow.⁶⁴ Nonetheless, no particular spatial frequencies could be associated to flows for [small gamma, Greek, dot above] = 0.043 and 0.14 s⁻¹, at least in a time-window of 150 min.

Fig. 8 Two-dimensional grayscale ¹H-NMR images acquired for lecithin organogel ϕ = 0.28 at T = 289 K. Interface patterns in steady state for applied [small gamma, Greek, dot above] = 0.07 s⁻¹ after (A) t = 35 min (γ = 147) and (B) t = 85 min (γ = 357). (C) Axial profiles (width = 15 mm) selected in the cell gap where the ¹H-NMR signal intensity has been averaged at rest (left) and from t = 5 min to t = 155 min at [small gamma, Greek, dot above] = 0.07 s⁻¹ (middle) and [small gamma, Greek, dot above] = 0.14 s⁻¹ (right) for comparison. (D) FT of ¹H-NMR intensity averaged in the selected profiles as a function of the spatial frequency.

Previous rheo-SANS experiments performed on the very same organogel composition revealed oscillatory dynamics of the shear-induced nematic order parameter, occurring already at low [small gamma, Greek, dot above] inside the stress plateau, which was analysed in terms of travelling waves of the director orientation profile along the circumference of the Couette cell.⁵³ The shear-induced nematic order parameter was also established in the high shear rate branch of the stress plateau.^48,49

We infer that the combination of both rheo-SANS and rheo-NMR results may indicate the presence of 3D Taylor-like vortices stacked along the vorticity direction, which have been also found in other wormlike micellar aqueous systems.^71–76

Structure of the flow field

NMR velocimetry experiments were carried out in Couette shear cell on lecithin organogel at micellar volume fraction ϕ = 28% and for imposed rate of deformation above the shear banding plateau. Velocity profiles along the entire gap were obtained in 44 min and collected in Fig. 9 for selected slices, parallel to the velocity gradient axis, and located to the bottom-center of the Couette cell, i.e. where the homogeneity of the static magnetic field was higher. The SEVI-NMR experiment was performed in the stationary state, which was controlled by monitoring the steady state viscosity on a shear flow rheometric experiment carried out in the same experimental conditions.

Fig. 9 Velocity profiles selected along the velocity gradient axis (see marked lines quoted at 60, 70 and 80 in the colour map image) and plotted vs. gap radius r = 1 mm with moving boundary at X = 0 and static wall at X = 1. Voxels with high flow velocity appear in light green. Velocity data were collected under stationary Couette flow and averaged for 44 min at [small gamma, Greek, dot above] = 10 s⁻¹ for lecithin organogel ϕ = 28% at T = 289 K. Data have been normalized with the velocity of inner cylinder, which was filled with a marker fluid. Dashed lines identify an abrupt change of slope occurring near X = 0.5 and solid line shows the velocity profile expected for a Newtonian fluid in the laminar regime.

To gain a reliable signal-to-noise ratio, the imposed shear rate could not be set lower than 10 s⁻¹, which was numerically equivalent to the velocity v₀ of the inner cylinder within the small gap approximation (v₀ ≅ [small gamma, Greek, dot above]r mm s⁻¹ for a gap size r = 1 mm). The time-averaged profiles shown in Fig. 9 indicated the presence near the moving rotor of a thick layer of fluid experiencing an almost constant velocity, albeit 20% smaller than the imposed shear rate. Then, after extending up to about half the gap width, the velocity decreased linearly without vanishing at the stationary outer boundary.

A similar scenario was reported by Hu et al.⁷⁷ on TTAA/NaSal micelles using particle image velocimetry, where a thick region of uniform velocity was found to develop at the inner rotating wall, followed by a steeper velocity gradient near to the stator. Those results were rationalised in terms of shear-induced structure associated to the non-homogeneous flow, behaving as a solid body in rotation with slippage at the walls.

Same phenomenon might occur in the present system as well, with the thick slip layer observed at the moving plane interpreted as evidence for a near rigid body motion. The slope of straight dashed line drawn in Fig. 9 was congruent to the one foreseen for a Newtonian fluid in laminar regime (solid line in the same figure). Actually, it should correspond to the velocity profile coming from the shear-aligned nematic state; stable at the imposed shear rate 10 s⁻¹ and located in the high [small gamma, Greek, dot above] branch of the stress plateau (see Fig. 3). On the other hands, minor slip effects occurring at the outer cylinder could be responsible for the nonzero velocity manifested by the fluid at the static wall.

Conclusions

Reverse lecithin WM represent an important reference fluid within non-ionic gel-forming surfactants, whose rheological response is unaffected by the presence of branches, which in turn allow additional stress release points.⁷⁸ Indeed, while most of aqueous WM systems made by non-ionic surfactants are characterized by the presence of micellar junctions (branches), reverse lecithin WM have been found to entangle in the form of unbranched micellar network.³⁹ A direct proof of branched systems ubiquitous in non-ionic aqueous micellar gels, is the observation of the type of phase separation: a fully branched micellar network phase separates into saturated network coexisting with a dilute surfactant solution, whereas the present reverse system evolves to a Winsor II-type phase separation where spherical swollen water-in-oil micelles coexist with excess water.⁴⁴

Therefore, in this work NMR micro-imaging and NMR velocimetry, integrated by both oscillatory and steady state conventional rheometry, have been applied for the first time on an oil-continuous shear-thinning wormlike micellar system. Dynamics oscillatory rheology signed the non-Maxwellian character of the investigated organogel viscoelastic material.

Stress relaxation measured after interrupted step strain experiments showed a two-step exponential decay compatible with the classical restoration of entanglements following chain retraction. For lecithin organogels in the concentrated isotropic phase, NMR imaging carried out for applied shear rates within the stress plateau, revealed a new phase nucleating inhomogeneously at the inner wall of the Couette cell, already a few minutes after flow inception and coexisting with the isotropic phase. Those features could be reminiscent of the formation of Taylor-like vortices spatially distributed along the vorticity axis. Besides, in correspondence of shear flow regimes realised above the stress plateau, NMR velocimetry showed sharp changes in velocity profiles across the gap of Couette cell as a consequence of slippage occurring near the moving inner cylinder and, in minor extent, at the stator as well. In conclusion, the present rheo-NMR investigation, carried out on a branch-free viscoelastic micellar network, can provide a valid experimental platform to test the micro-rheological properties of polymer-like self-assembled aggregates.

Acknowledgements

Financial supports from CSGI (Research Center for Colloids and Nanoscience, Florence, Italy) and MIUR-PRIN 411 2010–2011 (Prot. 2010BJ23 MN_006) are gratefully acknowledged.

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