Flow Of Wormlike Micellar Solutions Research Articles

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.

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.

Effect of micelle breakage rate on flows of wormlike micellar solutions through pore throats

Many practical applications such as enhanced oil recovery or groundwater remediation encounter the flow of viscoelastic wormlike micellar solutions (WLMs) through porous media. A model porous media, consisting of a microchannel with pore throats present in it, is often used to understand the flow dynamics of these complex fluids. This study performs an extensive numerical investigation to understand the complex flow behaviour of these WLMs through such a model porous media based on the two-species Vasquez–Cook–McKinley (VCM) model for micelles. Within the present range of conditions encompassed in this study, we find the existence of an elastic instability once the Weissenberg number exceeds a critical value as it was seen in many prior experimental and numerical studies dealing with polymer solutions. However, for the present case of a WLM solution, we observe that the micelle breakage rate greatly influences these instabilities. In particular, we observe that the intensity of this instability (characterized by the fluctuating flow field) increases with the Weissenberg number up to a critical value of it. Beyond that, it starts to decrease on further increment in the Weissenberg number. This is in contrast to that seen in a polymer solution where the flow field gradually transits to a more chaotic and turbulent-like state (the so-called elastic turbulence state) as the Weissenberg number gradually increases. Furthermore, we notice that the flow dynamics of these WLM solutions strongly depend on the type (symmetric or asymmetric), number, and spacing between two consecutive pore throats. Additionally, an extensive discussion on the pressure drop and relative viscosity is presented in the present study. Although this study is carried out for a model porous system, we hope it will facilitate a better understanding of the flow behaviour of wormlike micellar solutions in an actual porous media. • An elastic instability emerges once the Weissenberg number exceeds a critical value. • As the micelles are become progressively easy to break, the tendency of appearing the elastic instability decreases. • A non-monotonic trend in the flow behaviour is observed as the Weissenberg number gradually increases. • The elastic instability strongly depends on the throat type, number of throats, and the spacing between them.

Flow of wormlike micellar solutions through a long micropore with step expansion and contraction

In this study, an extensive numerical investigation has been carried out in order to understand the flow characteristics of a wormlike micellar (WLM) solution through a long micropore with step expansion and contraction. The VCM (Vasquez-Cook-McKinley) [P. A. Vasquez, G. H. McKinley, and P. L. Cook, “A network scission model for wormlike micellar solutions: I. Model formulation and viscometric flow predictions,” J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)] constitutive model has been used for the present WLM solution for predicting its rheological behavior and the governing equations, namely, mass and momentum equations along with the VCM constitutive model equations have been solved using the finite-volume method based open source code OpenFOAM. Within the range of conditions encompassed in this study, different flow regimes have been observed in the pore geometry, for instance, Newtonian like regime, lip vortex formation regime, unsteady and vortex merging regime, etc. In particular, an elastic instability regime has been observed in the pore geometry, and the onset of this regime is accentuated with the increasing values of the Weissenberg number and decreasing values of the nonlinear VCM model parameter ξ. Apart from the flow pattern, a detailed discussion on the distribution of the wormlike micellar concentration, principal stress difference, apparent relative viscosity, etc., is also presented. Finally, a good qualitative agreement (in terms of the flow pattern) has been found between the present simulations and the corresponding experiments.

Flow of wormlike micellar solutions around microfluidic cylinders with high aspect ratio and low blockage ratio.

We employ time-resolved flow velocimetry and birefringence imaging methods to study the flow of a well-characterized shear-banding wormlike micellar solution around a novel glass-fabricated microfluidic circular cylinder. In contrast with typical microfluidic cylinders, our geometry is characterized by a high aspect ratio α = H/W = 5 and a low blockage ratio β = 2r/W = 0.1, where H and W are the channel height and width, and the cylinder radius r = 20 μm. The small cylinder radius allows access up to very high Weissenberg numbers 1.9 ≤ Wi = λMU/r ≤ 3750 (where λM is the Maxwell relaxation time) while inertial effects remain entirely negligible (Reynolds number, Re < 10-4). At low Wi values, the flow remains steady and symmetric and a birefringent region (indicating micellar alignment and tensile stress) develops downstream of the cylinder. Above a critical value Wic ≈ 60 the flow transitions to a steady asymmetric state, characterized as a supercritical pitchfork bifurcation, in which the fluid takes a preferential path around one side of the cylinder. At a second critical value Wic2 ≈ 130, the flow becomes time-dependent, with a characteristic frequency f0 ≈ 1/λM. This initial transition to time dependence has characteristics of a subcritical Hopf bifurcation. Power spectra of the measured fluctuations become complex as Wi is increased further, showing a gradual slowing down of the dynamics and emergence of harmonics. A final transition at very high Wic3 corresponds to the re-emergence of a single peak in the power spectrum but at much higher frequency. We discuss this in terms of possible flow-induced breakage of micelles into shorter species with a faster relaxation time.

Sphere sedimentation in wormlike micelles: Effect of micellar relaxation spectrum and gradients in micellar extensions

We report experiments on the flow of wormlike micellar solutions based on cetylpyridinium chloride/sodium salicylate past a falling sphere via a combination of particle tracking velocimetry, particle image velocimetry, rheology, and flow induced birefringence (FIB). Recent studies have shown that beyond a critical extensional Deborah number, a falling sphere in wormlike micelles never reaches a constant terminal velocity; instead, it settles with an unsteady velocity. This behavior is linked to the wormlike micellar chain scission in the wake of the sphere. Similar instabilities in viscoelastic polymer solutions, where polymer chain scission is highly unlikely, are thought to be the results of a single-mode relaxation spectrum of the polymer chains or the asymmetry in the polymer chain extensions on the flanks of the falling sphere. In this paper, we examine the effect of micellar relaxation spectrum and gradients in micellar extensions on sphere instability in wormlike micelles over a wide range of flow parameters (10−2 &amp;lt; DeE &amp;lt; 40.7 and 10−6 &amp;lt; Re &amp;lt; 10). In wormlike micelles with a single-mode relaxation spectrum, the sphere instability occurs for DeE ≥ 2.6. However, for similar conditions (2.5 ≤ DeE ≤ 40.7 and 10−2 &amp;lt; Re &amp;lt; 10), spheres never exhibit unsteady motion in the wormlike micelles with a broad spectrum of relaxation times. This indicates the importance of the micellar relaxation spectrum on dynamics of sphere sedimentation in wormlike micelles. We show that a criterion based on the ratio of dissipated energy to the stored elastic energy of micelles can successfully describe the effect of micellar relaxation spectrum on sphere sedimentation dynamics. In addition, for conditions that give rise to sphere instability, FIB indicates that micellar extensions on sphere sideways are perfectly symmetric.

Elastic instability and secondary flow in cross-slot flow of wormlike micellar solutions

In this work, we focus on modeling the flow of wormlike micellar solutions in a cross-slot device. In particular, we investigate the role that the breakage of wormlike micelles plays in the formation of lip vortices and the development of an asymmetric elastic instability. The cross-slot induces a planar elongational flow field around the stagnation point in the center of the geometry, and a shear-dominated flow in the inlet and outlet arms. The extensional flow can induce the emergence of a bifurcation, in which the symmetric flow undergoes an instability and becomes asymmetric at sufficiently large flow rates. We further show that this instability can be completely suppressed by creating micelles that are easier to break under imposed stretching. Furthermore, at larger flow rates, unlike comparable simulations of polymer solutions, the asymmetric flow remains steady in agreement with experiments. In addition, the shear flow can induce the formation of a recirculation region in the inlet arm along the channel wall directly upstream of the corner. In particular, we reveal the possibility of controlling the vortex regions via flow-induced breakage; as the chains become easier to break, the degree of shear thinning increases and the size of the vortices decreases. Ultimately, our predictions show that chain scission plays an important role in altering fluid flow.

Role of chain scission in cross-slot flow of wormlike micellar solutions

The role of chain scission is investigated numerically in the symmetry breaking of the flow of wormlike micellar solutions in a cross-slot geometry.

A study of pressure-driven flow of wormlike micellar solutions through a converging/diverging channel

The pressure-driven flow of a macroscale network model, which was derived from mescoscale network considerations and was developed to describe wormlike micellar mixtures, the Vasquez, Cook, McKinley (VCM) model [Vasquez et al., J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)], is investigated in a periodically varying, converging/diverging channel. The VCM model consists of a coupled system of nonlinear partial differential equations describing two elastically active breaking and reforming micellar species. Previous analysis of the VCM model has shown that it captures both purely shear and purely extensional flow behaviors of wormlike micellar solutions. In this paper, the combined effects of shear and extension are probed by simulating the flow in a converging/diverging channel. Using domain perturbation analysis, the model equations are perturbed about the straight channel geometry thereby describing the flow through the perturbed, wavy wall geometry. The resulting first order perturbed system of (linear) partial differential equations is solved numerically using the overlapping Schwarz alternating domain decomposition method. The analysis shows that even in this simple perturbation, the VCM model is capable of capturing signatures of experimental flow behaviors of wormlike micelles through converging geometries. These signatures include the deviation from Newtonian fore-aft symmetry as well as a nonmonotonic relationship between the first normal stress difference and the extension rate along the centerline.

Flow of wormlike micellar solutions around confined microfluidic cylinders.

Wormlike micellar (WLM) solutions are frequently used in enhanced oil and gas recovery applications in porous rock beds where complex microscopic geometries result in mixed flow kinematics with strong shear and extensional components. Experiments with WLM solutions through model microfluidic porous media have revealed a variety of complex flow phenomena, including the formation of stable gel-like structures known as a Flow-Induced Structured Phase (FISP), which undoubtedly play an important role in applications of WLM fluids, but are still poorly understood. A first step in understanding flows of WLM fluids through porous media can be made by examining the flow around a single micro-scale cylinder aligned on the flow axis. Here we study flow behavior of an aqueous WLM solution consisting of cationic surfactant cetyltrimethylammonium bromide (CTAB) and a stable hydrotropic salt 3-hydroxy naphthalene-2-carboxylate (SHNC) in microfluidic devices with three different cylinder blockage ratios, β. We observe a rich sequence of flow instabilities depending on β as the Weissenberg number (Wi) is increased to large values while the Reynolds number (Re) remains low. Instabilities upstream of the cylinder are associated with high stresses in fluid that accelerates into the narrow gap between the cylinder and the channel wall; vortex growth upstream is reminiscent of that seen in microfluidic contraction geometries. Instability downstream of the cylinder is associated with stresses generated at the trailing stagnation point and the resulting flow modification in the wake, coupled with the onset of time-dependent flow upstream and the asymmetric division of flow around the cylinder.

Vortex ring formation in oscillatory pipe flow of wormlike micellar solutions

The destabilization of rectilinear oscillatory pipe flow and the formation of vortex rings in a wormlike micellar solution, CPyCl/NaSal [100:60] mM, oscillated in a vertical cylinder of large aspect ratio, has been studied by means of time-resolved-particle image velocimetry measurements in a meridional plane of the cylinder. The flow was inertialess (Re<1) and dominated by fluid elasticity (De≫1). The oscillatory pipe flow of a Newtonian fluid under equivalent conditions would remain rectilinear and laminar. For the micellar solution, instead, the reversing character of the rectilinear flow induces vortex ring formation. The stability boundaries between rectilinear, axisymmetric-vortical, and non-axisymmetric-vortical flows in the middle region of the cylinder have been determined from the root-mean-square fluctuations of the measured vertical and radial velocity components. Measurements performed over the whole tube length reveal that the flow destabilization and the subsequent formation of vortex rings is favored at the bottom part of the cylinder, close to the driving piston. As the driving amplitude is increased, the vortical flow expands vertically upwards, giving rise to a number of coaxial toroidal vortices distributed over the vertical pipe. On short-time scales these axisymmetric vortex rings are periodic in time with the periodicity of the driving. On long time scales, much longer than the relaxation time of the fluid, we uncover an additional temporal evolution of the vortical flow which makes the spatiotemporal structure of the oscillatory flow more involved.

Stagnation point flow of wormlike micellar solutions in a microfluidic cross-slot device: Effects of surfactant concentration and ionic environment

We employ the techniques of microparticle image velocimetry and full-field birefringence microscopy combined with mechanical measurements of the pressure drop to perform a detailed characterization of the extensional rheology and elastic flow instabilities observed for a range of wormlike micellar solutions flowing through a microfluidic cross-slot device. As the flow rate through the device is increased, the flow first bifurcates from a steady symmetric to a steady asymmetric configuration characterized by a birefringent strand of highly aligned micellar chains oriented along the shear-free centerline of the flow field. At higher flow rates the flow becomes three dimensional and time dependent and is characterized by aperiodic spatiotemporal fluctuations of the birefringent strand. The extensional properties and critical conditions for the onset of flow instabilities in the fluids are highly dependent on the fluid formulation (surfactant concentration and ionic strength) and the resulting changes in the linear viscoelasticity and nonlinear shear rheology of the fluids. By combining the measurements of critical conditions for the flow transitions with the viscometric material properties and the degree of shear-thinning characterizing each test fluid, it is possible to construct a stability diagram for viscoelastic flow of complex fluids in the cross-slot geometry.

Experiments on the laminar oscillatory flow of wormlike micellar solutions

We report new experimental results of the oscillatory flow of a solution of giant micelles in a narrow vertical tube. We explore small driving amplitudes (laminar flow) and a large range of driving frequencies. High-resolution particle image velocimetry measurements of the flow field in a meridional plane of the tube show that the velocity magnitude at the tube axis peaks at well-defined resonance frequencies, where the phase lag with the forcing changes abruptly. The velocity field is highly inflectional and eventually exhibits some hints of shear banding. The results are compared with theoretical predictions based on the upper-convected Maxwell and Oldroyd-B models of the linear shear rheology of the solution, and observed coincidences and discrepancies are discussed in detail.

Elastic instabilities in a microfluidic cross-slot flow of wormlike micellar solutions

We present a series of experiments involving an elastic instability that occurs with the flow of wormlike micellar solutions in a microfluidic cross-slot device. We use four different concentrations of an aqueous solution of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal); two highly viscoelastic and two weakly viscoelastic. Flow in the microfluidic cross-slot device is examined using birefringence and PIV measurements. With all of the solutions we observe the formation of a birefringent band along the outflow axis, the intensity of which increases with the flow rate. In the two highly viscoelastic solutions, as the flow rate increases, the instability results in flow transitioning from a stable symmetric flow to a stable asymmetric flow, to an unsteady asymmetric flow. With the weakly viscoelastic solutions the instability results in the flow transitioning directly from a stable symmetric flow to an unsteady flow. The critical Weissenberg numbers at which the transitions occur, increase with increasing elasticity number (defined as the ratio of the Weissenberg number to the Reynolds number). With the two highly viscoelastic solutions we also observe the formation of lip vortices along the walls of the inlet channels. For one of the highly viscoelastic solutions the symmetry-breaking occurs before the formation of the secondary flow, whereas in another solution the secondary flow develops prior to the symmetry-breaking. This indicates that these instabilities are complex phenomena, whose behavior is likely influenced by a combination of factors such as Weissenberg number, inertial effects, and rheological behavior of the micellar solutions.

Pressure-driven flow of wormlike micellar solutions in rectilinear microchannels

AbstractIn this paper the inhomogeneous response of the (two species) VCM model (Vasquez et al., A network scission model for wormlike micellar solutions. I. Model formulation and homogeneous flow predictions, J. Non-Newtonian Fluid Mech. 144 (2007) 122–139) is examined in steady rectilinear pressure-driven flow through a planar channel. This microstructural network model incorporates elastically active network connections that break and reform mimicking the behavior of concentrated wormlike micellar solutions. The constitutive model, which includes non-local effects arising from Brownian motion and from the coupling between the stress and the microstructure (finite length worms), consists of a set of coupled nonlinear partial differential equations describing the two micellar species (a long species ‘A’ and a shorter species ‘B’) which relax due to reptative and Rouse-like mechanisms as well as rupture of the long micellar chains. In pressure-driven flow, the velocity profile predicted by the VCM model deviates from the regular parabolic profile expected for a Newtonian fluid and exhibits a complex spatial structure. An apparent slip layer develops near the wall as a consequence of the microstructural boundary conditions and the shear-induced diffusion and rupture of the micellar species. Above a critical pressure drop, the flow exhibits shear banding with a high shear rate band located near the channel walls. This pressure-driven shear banding transition or ‘spurt’ has been observed experimentally in macroscopic and microscopic channel flow experiments. The detailed structure of the shear banding profiles and the resulting flow curves predicted by the model depend on the magnitude of the dimensionless diffusion parameter. For small channel dimensions, the solutions exhibit ‘non-local’ effects that are consistent with very recent experiments in microfluidic geometries (Masselon et al., Influence of boundary conditions and confinement on non local effects in flows of wormlike micellar systems, Phys. Rev. E 81 (2010) 021502).

Extensional flow of wormlike micellar solutions

Abstract We consider the inhomogeneous extensional response of a new constitutive model, the VCM model [Vasquez, et al., 2007. A network scission model for wormlike micellar solutions I: model formulation and homogeneous flow predictions. J. Non-Newt. Fluid Mech. 144, 122–139] that has been developed to describe concentrated solutions of wormlike micelles. The time dependent numerical analysis is carried out in a simplified slender filament formulation appropriate for transient elongational flows of complex fluids. The simulations show that, beyond a critical extension rate, elongating filaments of a micellar fluid described by the VCM model exhibit a dramatic and sudden rupture event as a result of the scission of the entangled wormlike chains. The computations capture many of the features of the high-speed rupture process observed experimentally [Bhardwaj, et al., 2007. Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions. J. Rheol. 51, 693–719] in filament stretching experiments with wormlike micelle solutions. The highly localized rupture predicted by the VCM model and the corresponding evolution in the tensile force within the filament is contrasted with the familiar and more gradual necking responses predicted by the upper convected Maxwell and Giesekus models under equivalent kinematic boundary conditions.

Transition to shear banding in pipe and Couette flow of wormlike micellar solutions

We used both conventional rheometry and nuclear magnetic resonance (NMR) velocimetry to study shear banding in a solution of 200 mM cetylpyridinium chloride and 120 mM sodium salicylate in 0.5 M sodium chloride. The solution behaved as a Maxwell fluid up to frequencies of 10 Hz. Theoretical predictions of critical strain rate and shear stress were in good agreement with measurements obtained using controlled strain rate rheometry. Using NMR velocimetry, we observed convincing evidence of shear banding in capillary flow with a band of very high, approximately constant, shear rate next to the wall that grew in thickness with increasing apparent shear rate. We believe that the shear rate in this band (∼600 s−1) marks the beginning of the hypothesized high shear rate limb of the flow curve. We also observed shear banding in both the cylindrical Couette and cone-and-plate geometries. Shear banding started at shear rates that were approximately the same as the critical shear rate measured with the mechanical rh...

Capillary rheometry of micellar aqueous solutions

In this work, the capillary flow of wormlike micellar solutions was studied in detail. Flow curves obtained with capillaries of different sizes for surfactant aqueous solutions at various concentrations, were analyzed with particular attention to the regions of flow instability. It was found that to observe unstable flow a critical residence time of the solution in the capillary is needed, in addition to a critical shear stress value. At specific surfactant concentrations, a plateau-like region was observed for sufficiently long residence times of the liquid under flow, either in the capillary or in a cone and plate rheometer. For shear rates higher than those of the plateau region, the expected upturn on the flow curves was observed and studied. The flow curves in this regime were dependent on the capillary diameter in an opposite way as found in the presence of slip, i.e., adherence appears to occur. The flow instabilities (observed as unstable pressure at the capillary entrance and a variable flow rate at the exit) were detected even for the lowest concentration solution where the plateau region was not apparent. The flow instabilities took place completely in the absence of slip. A remarkable effect was observed in the solution with the higher surfactant concentration using a flow system that allows long residence times (about 1 h). In this case, within a small window of shear stresses, a dramatic increase in flow rate accompanied by a large drop in the pressure measured at the capillary entrance was observed. After a minimum, the pressure increased again up to the initial stress and a new cycle began subsequently. This result is consistent with similar observations made in cone and plate or Couette geometries, which are attributed to the presence of `shear bands'.