New insights on fumed colloidal rheology—shear thickening and vorticity-aligned structures in flocculating dispersions

We investigate the rheology of dilute dispersions of fumed colloidal particles with attractive interactions in hydrocarbon liquids. Surprisingly, these systems display shear thickening due to the breakdown of densified flocs and a concomitant increase in the effective volume fraction of the fractal particles in the fluid. We show that this shear thickening is controlled by a critical stress and accompanied by a positive increase in the first normal stress difference, N ₁, at the shear thickening transition. This is in contrast to the well-known hydrocluster mechanism of shear thickening in concentrated hard-sphere and repulsive systems. Gel elasticity depends strongly on the stress applied to suspensions in preshear, scaling roughly as \(G'\sim\sigma_{\text{preshear}}^{2}\). We propose a simple model to account for these results in terms of the cluster number density determined by the preshear stress. At low shear rates, vorticity-aligned aggregates are present at \(\dot\gamma\approx 10^0 {\rm{s}}^{-1}\) . In this regime, the system displays a small but noticeable increase in viscosity on increasing shear rate. We investigate the effect of tool roughness and find that wall slip is not responsible for the observed phenomena. Instead, the increase in the apparent viscosity results from increased flow resistance due to the presence of gap-spanning log-like flocs in rolling flow.     

Non-Newtonian flow in microporous structures under the electroviscous effect

Single phase non-Newtonian microporous flow combined with the electroviscous effect is investigated in the pore-scale under conditions of various rheological properties and electrokinetic parameters. The lattice Boltzmann method is employed to solve both the electric potential field and flow velocity field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends on both the fluid rheological behavior and pore surface area ratio significantly. For the shear thinning fluid with power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electrovicous effect plays a more important role compared to the Newtonian fluid and shear thickening fluid. The high pore surface area ratio in the porous structure increases the electroviscous force and the induced flow resistance becomes important even to the flow of Newtonian and shear thickening fluids.     

On the shear-thickening behaviour of dilute solutions of chain macromolecules

The shear thickening observed in laminar Poiseuille flow for dilute solutions of polystyrene of high molecular weight in decalin is studied as a function of concentration, molecular weight and shear rate. The experiments show the existence of four invariants, i.e. two critical Deborah numbers, a critical viscosity ratio, and a critical hydrodynamic dissipated energy, in terms of which a mechanism of this shear thickening can be proposed. It involves a permanent deformation of the macro molecules above a critical shear.     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Electrorheological properties of PDMS/carbon black suspensions under shear flow

Suspensions of polydimethylsiloxane (PDMS) containing low amounts (1 wt.% or less) of a highly conducting carbon black (CB) filler are rendered conductive and exhibit electrorheological (ER) responses under shear flow when exposed to an externally applied AC electric field. The presence of columnar structures, consisting of CB particles aligned in the direction of the electric field is evidenced through optical microscopy experiments. The appearance of yielding behavior and positive ER response, manifested by an increase in the viscosity of the suspensions, depend strongly on the filler loading, strength of the electric field, magnitude of the shear field, and viscosity of the medium. The responses are stronger at low filler loadings, below the percolation threshold, and at very low shear rates, where the microstructure of the dispersed phase remains intact. At higher shear rates, corresponding to Mason numbers (Mn) above 1, the structure is disrupted and thus does not contribute to the observed shear stress. The rheological characterization is accompanied with admittance measurements, to demonstrate that the induced polarization forces between particles lead to the formation of electrically conductive structures within the polymer matrix. A critical comparison with the qualitative predictions based on the theory of induced dipole–dipole interactions shows that the theory is valid for these dilute systems.     

Compound wall treatment with low‐Re turbulence model

A generalized treatment for the wall boundary conditions relating to turbulent flows is developed that blends the integration to a solid wall with wall functions. The blending function ensures a smooth transition between the viscous and turbulent regions. An improved low Reynolds number k?ε model is coupled with the proposed compound wall treatment to determine the turbulence field. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and Schwarz' inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence. Computations with fine and coarse meshes of a few flow cases yield appreciably good agreement with the direct numerical simulation and experimental data. The method is recommended for computing the complex flows where computational grids cannot satisfy a priori the prerequisites of viscous/turbulence regions. Copyright © 2011 John Wiley & Sons, Ltd.     

Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study

This paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non‐linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non‐Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear‐thinning and shear‐thickening characteristics of the non‐Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid. Copyright © 2009 John Wiley & Sons, Ltd.     

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclét number and Debye–Hückel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.     

Effects of electric fields and volume fraction on the rheology of hematite/silicone oil suspensions

Electrorheological (ER) fluids composed of iron(III) oxide (hematite) particles suspended in silicone oil are studied in this work. The rheological response has been characterized as a function of field strength, shear rate and volume fraction. The dielectric properties of the suspensions were first studied in order to get information about the conductivity of the solid. Rheological tests under a.c. electric fields elucidated the influence of the electric field strength and volume fraction on the field-dependent yield stress. It was found that this quantity scales as a square power law in both cases. The viscosities of electrified suspensions were found to increase by several orders of magnitude as compared to the unelectrified suspension at low shear rates, although at high shear rates hydrodynamic effects become dominant and no effects of the electric field on the viscosity are observed. The ER behaviour of the suspensions was analysed by considering the fundamental forces (of hydrodynamic and electrostatic origin) acting on the particles and it is found that, at a given volume fraction, all the dependencies of relative viscosity on shear rate and field strength can be described by a single function of the Mason number, Mn. Finally, two different chain models were used to explain the shear-thinning behaviour observed: rheological measurements showed a power-law dependence of relative viscosity decrease on the Mason number, _F~Mn, with –0.95.     

Large eddy simulations of flow interference between two unequal sized square cylinders

A uniform flow past two unequal sized square cylinders arranged in a side-by-side pattern and at a Reynolds number of 50,000 has been investigated using large eddy simulation (LES) technique. The modelling of sub-grid scales of turbulence is done using the Smagorinsky model. The effect of the transverse gap ratio (T/D) on the flow characteristics has been studied. Numerical simulations are carried out for five different transverse gap ratios (T/D), namely 1.120, 1.250, 1.375, 1.750 and 2.500. Results in terms of the aerodynamic forces, Strouhal number, mean base pressure coefficient, streamlines, vorticity, surface pressure distribution, normal and shear stresses are presented. A shift in the stagnation point for the small square cylinder from the centre of its front face towards its gap side is seen at smaller T/D ratios. The presence of a jet-like flow seen in the gap side is more pronounced at T/D = 1.12. A biased gap side flow towards the near wake of the small square cylinder is seen at smaller T/D ratios. No interference effect is seen at T/D = 2.5. The flow behaviour is similar to that of the isolated square cylinder at this gap ratio.     

A fast non‐Fickian particle‐tracking diffusion simulator and the effect of shear on the pollutant diffusion process

This paper presents a fast method for the generation of non‐Fickian particle paths within a particle‐tracking pollutant diffusion model based on a Fourier spectral representation of fractional Brownian motion (fBm), a generalization of ordinary Brownian motion. Correlated diffusive components in a particle‐tracking algorithm are modelled using fBm increments that have long‐range correlations over numerous spatial and/or temporal scales; hence producing non‐Fickian diffusion. A fast algorithm to generate fBm and its increment by using its power spectral density S(f) in a fast Fourier transform algorithm is given. A general equation for the scaling of fBm within a velocity flow field with simple linear shear is presented. An initial numerical study of the nature of fBm shear dispersion has been conducted by incorporating fBm increments into a non‐Fickian particle‐tracking algorithm. It is shown that the effect of simple (i.e. linear) shear on the diffusion process is to produce enhanced diffusive phenomena with the longitudinal spreading of the plume scaling with exponent ∼1+H, where H is the Hurst exponent used to describe fBm. Finally, a more complex shear zone at the entrance of a coastal bay model is investigated using both a traditional particle‐tracking method and the fBm‐based method. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparative study of the electrorheological effect in suspensions of needle-like and isotropic cerium dioxide nanoparticles

A novel approach to the analysis of the electrorheological effect is proposed, based on the expansion of dimensionless relative shear stress as function of electric field strength in the power series \( {\tau}_{\mathrm{rel}}=\frac{\tau_E}{\tau }=1+\frac{\alpha }{\tau }E+\frac{\beta }{\tau }{E}^n \). The application of this approach to investigation of the electrorheological effect in suspensions of isotropic and needle-like CeO₂ nanoparticles in polydimethylsiloxane has revealed that the polynomial coefficients can be judged as a measure of the efficiency of transformation of electrical energy into mechanical energy. The values of α and β coefficients depend on the shape and concentration of filler particles, as well as on the shear rate. The value and the sign of these coefficients determine both the magnitude of the electrorheological effect and the type of dependence of the shear stress (linear or power law) on the strength of the electric field. It has been shown that the values of α and β coefficients for the electrorheological fluids with needle-like particles are greater than for fluids with isotropic particles (at the same concentration of suspensions), which is associated with the different polarization of particles in the applied electric field.

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Graphical abstract A novel approach to the analysis of the electrorheological effect is proposed.

     

Extended thermodynamics of a relativistic plasma with finite electric conductivity

A system of equations for relativistic m.h.d, with finite electric conductivity and no heat flux is proposed, starting from the properties of the systems of conservation laws compatible with a supplementary balance law (entropy balance) with convex density (symmetric-hyperbolic systems). The electric current density is treated as a new field variable which contributes to non equilibrium entropy density (extended thermodynamics). The result is a theory in which only one new constitutive function, representing entropy increment respect to equilibrium, is necessary to characterize the properties of the medium related to electric conductivity.G.N.F.M. of the C.N.R.     

Evaluation of the Effect of Thermal Oxidation and Moisture on the Interfacial Shear Strength of Unidirectional IM7/BMI Composite by Fiber Push-in Nanoindentation

Fiber push-in nanoindentation is conducted on a unidirectional carbon fiber reinforced bismaleimide resin composite (IM7/BMI) after thermal oxidation to determine the interfacial shear strength. A unidirectional IM7/BMI laminated plate is isothermally oxidized under various conditions: in air for 2 months at 195 °C and 245 °C, and immersed in water for 2 years at room temperature to reach a moisture-saturated state. The water-immersed specimens are subsequently placed in a preheated environment at 260 °C to receive sudden heating, or are gradually heated at a rate of approximately 6 °C/min. A flat punch tip of 3 μm in diameter is used to push the fiber into the matrix while the resulting load-displacement data is recorded. From the load-displacement data, the interfacial shear strength is determined using a shear-lag model, which is verified by finite element method simulations. It is found that thermal oxidation at 245 °C in air leads to a significant reduction in interfacial shear strength of the IM7/BMI unidirectional composite, while thermal oxidation at 195 °C and moisture concentration have a negligible effect on the interfacial shear strength. For moisture-saturated specimens under a slow heating rate, there is no detectable reduction in the interfacial shear strength. In contrast, the moisture-saturated specimens under sudden heating show a significant reduction in interfacial shear strength. Scanning electron micrographs of IM7/BMI composite reveal that both thermal oxidation at 245 °C in air and sudden heating induced microcracks and debonding along the fiber/matrix interface, thereby weakening the interface, which is the origin of failure mechanism.     

Electroviscous effect on non-Newtonian fluid flow in microchannels

Understanding non-Newtonian flow in microchannels is of both fundamental and practical significance for various microfluidic devices. A numerical study of non-Newtonian flow in microchannels combined with electroviscous effect has been conducted. The electric potential in the electroviscous force term is calculated by solving a lattice Boltzmann equation. And another lattice Boltzmann equation without derivations of the velocity when calculating the shear is employed to obtain flow field. The simulation of commonly used power-law non-Newtonian flow shows that the electroviscous effect on the flow depends significantly on the fluid rheological behavior. For the shear thinning fluid of the power-law exponent n < 1, the fluid viscosity near the wall is smaller and the electroviscous effect plays a more important role. And its effect on the flow increases as the ratio of the Debye length to the channel height increases and the exponent n decreases. While the shear thickening fluid of n > 1 is less affected by the electroviscous force, it can be neglected in practical applications.     

An apparent viscosity function for shear thickening fluids

A new apparent viscosity function for shear thickening fluids is proposed, contemplating the three characteristic regions typically exhibited by these materials: slight shear thinning at low shear rates, followed by a sharp viscosity increase over a threshold shear rate value (critical shear rate), and a subsequent pronounced shear thinning region at high shear rates. The proposed function has a continuous derivative, making it appropriate in numerical simulations. Moreover, the function is shown to provide an excellent fit to several independent experimental data sets.     

Shear-thickening behavior of high molecular weight poly(ethylene oxide) solutions

Simple shear rheological properties of solutions of a high molecular weight (8 × 10⁶ g/mol) poly(ethylene oxide) (PEO) and its mixtures with sodium dodecyl sulfate (SDS) have been studied. Shear-thickening effects set in at a critical shear rate for PEO solutions. This particular behavior has not been reported for aqueous solutions of PEO, to our knowledge. The effect is attributed to PEO flow-induced self-aggregation. The experiments were performed in different operation modes (strain rate and stress controlled) and with different geometries (double wall Couette and Couette) and identical viscosities were obtained, which rules out flow instabilities as possible cause for the shear-thickening effect. Shear thickening was observed in the temperature range 15–50°C. Flow-induced PEO degradation occurs for shear rates in the shear-thickening regime, which indicates substantial chain deformation and accumulated stresses in the molecule when shear thickening occurs. Addition of SDS to the PEO solutions induces the formation of surfactant polymer complexes that preserve the characteristic shear-thickening effect.     

Dynamic properties of shear thickening colloidal suspensions

The transient shear rheology (i.e., frequency and strain dependence) is compared to the steady rheology for a model colloidal dispersion through the shear thickening transition. Reversible shear thickening is observed and the transition stress compares well to theoretical predictions. Steady and transient shear thickening are observed to occur at the same value of the average stress. The critical strain for shear thickening is found to depend inversely on the frequency at fixed applied stress for low frequencies (high strains), but is limited to an apparent minimum critical strain at higher frequencies. This minimum critical strain is shown to be an artifact of slip. Lissajous plots illustrate the transition in material properties through the shear thickening transition, and the energy dissipated by a shear thickening suspension is analyzed as a function of strain amplitude.