The effect of wall depletion on the rheology of microfibrillated cellulose water suspensions by optical coherence tomography

Rheology of microfibrillated cellulose (MFC) water suspensions was characterized with a rotational rheometer, augmented with optical coherence tomography (OCT). To the best of the authors’ knowledge, this is the first time the behavior of MFC in the rheometer gap was characterized by this real-time imaging method. Two concentrations, 0.5 and 1 wt% were used, the latter also with 10^?3 and 10^?2 M NaCl. The aim was to follow the structure of the suspensions in a rotational rheometer during the measurements and observe wall depletion and other factors that can interfere with the rheological results. The stepped flow measurements were performed using a transparent cylindrical measuring system and combining the optical information to rheological parameters. OCT allows imaging in radial direction from the outer geometry boundary to the inner geometry boundary making both the shear rate profile and the structure of the suspension visible through the rheometer gap. Yield stress and maximum wall stress were determined by start-up of steady shear and logarithmic stress ramp methods and they both reflected in the stepped flow measurements. Above yield stress, floc size was inversely proportional to shear rate. Below the yield stress, flocs adhered to each other and the observed apparent constant shear stress was controlled by flow in the depleted boundary layer. With higher ionic strength (10^?2 M NaCl), the combination of yield stress and wall depletion favored the formation of vertical, cylindrical, rotating floc structures (rollers) coupled with a thicker water layer originating at the suspension—inner cylinder boundary at low shear rates.     

Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

On the wall slip of polymer blends

The slip flow of the polypropylene (PP)/poly[ethylene‐co‐(vinyl acetate)] (EVA) system was studied in a capillary rheometer for shear rates of 40–1000 s^?1 at four temperatures. Three dies made of aluminum with a length/diameter (L/D) ratio of 15 and diameters of 1.59, 1.19, and 0.79 mm provided the flow data. Calculations of the slip velocity by the Mooney method showed power‐law behavior with the stress. Blends were prepared at various proportions of PP and EVA for observation of the variation of the slip velocity for different compositions and temperatures. Direct microscopic observations of the slip layer on extruded samples showed domains of the dispersed phase unevenly distributed between the slip layer and the core and provided estimates of the thickness of the layer adjacent to the capillary wall. Results showed that the viscosity in the slip layer was 10–100 times lower than that in the bulk for the same value of the shear stress. In terms of the extrapolation length, the development of the slip layer was the result of different disentanglement dynamics of the molecules in the slip layer in comparison with those in the bulk. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 303–316, 2002     

Structure and rheological behavior of highly charged colloidal particles in a cylindrical pore I. Effect of pore size

In this work we performed nonequilibrium Brownian dynamics (NEBD) computer simulations of highly charged colloidal particles in diluted suspension under a parabolic flow in cylindrical pores. The influence of charged and neutral cylindrical pores on the structure and rheology of suspensions is analyzed. A shear-induced disorder-order-disorder-like transition was monitored for low shear rates and small pore diameters. We calculate the concentration profiles, axial distribution functions, and axial-angular pair correlation functions to determine the structural properties at steady state for a constant shear flow for different pore sizes and flow strengths. Similar behavior has been observed in a planar narrow channel in the case of charged interacting colloidal particles (M.A. Valdez, O. Manero, J. Colloid Interface Sci. 190 (1997) 81). The mobility of the particles in the radial direction decreases rapidly with the flow and becomes practically frozen. The flow exhibits non-Newtonian shear thinning behavior due to interparticle interactions and particle-wall interaction; the apparent viscosity is lower as the pore diameter decreases, giving rise to an apparent slip in the colloidal suspension. The calculated slip velocity was higher than that obtained in a rectangular slit under shear flow.     

Effect of cationic polymethacrylates on the rheology and flocculation of microfibrillated cellulose

Using two cationic methacrylate polymers: poly([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide) (PDMQ) and poly[(stearyl methacrylate)-stat-([2-(methacryloyloxy)ethyl] trimethyl ammonium iodide)] (PSMA13Q), we modified microfibrillated cellulose (MFC) water suspensions. The aim was to affect the flocculation and rheological behavior of the MFC suspension. PDMQ is a strongly cationic polymer while PSMA13Q, also a cationic polymer, contains hydrophobic segments. We studied the MFC/polymer suspension rheological properties with a rotational rheometer in oscillatory and flow measurements. To observe structural changes in suspensions at different shear rates, we measured flow curves with transparent outer geometry and photographed the sample with a digital camera. The oscillatory measurements showed that a small amount of the cationic PDMQ in the MFC suspension strengthened the gel, whereas a small amount of amphiphilic PSMA13Q weakened it. Increased amounts of either polymer increased the gel strength. PSMA13Q also changed the rheological character of the MFC suspension turning it more fluid-like. When we photographed the flow curve measurement, we saw a clear change in the floc structure. This floc structure rupture coincided with a transient region in the flow curve.     

Investigation of the Wall Slip Effect in Highly Concentrated Disperse Systems by Means of Non-Invasive UVP-PD Method in the Pressure Driven Shear Flow1

A novel in-line UVP-PD non-invasive rheological measuring technique was introduced for rheological analysis of highly concentrated disperse systems. The method is based on a combination of the Ultrasonic Pulsed Echo Doppler technique (UVP, Ultrasound Velocity Profiler) and the pressure difference (PD) method. The rheological properties were derived from simultaneous recording and on-line analysis of the velocity and related radial shear stress profiles across a circular channel. Wall slip velocity was extrapolated from the on-line fit and monitored on-line simultaneously with the flow index. Two effects were found and preliminarily analyzed. The first effect refers to a transition from strongly non-Newtonian to Newtonian flow velocity profile while increasing in the absolute flow velocity. The second flow effect refers to an abrupt reduction of the wall slip velocity while increasing the absolute flow velocity. Considerable discrepancy was found between the results of the in-line UVP-PD measurement in pressure driven shear flow and the results of the conventional rheometry.     

Effect of wall slip on the shear flow of a polymer in a channel with a wavy bottom

The effect of stick and wall slip boundary conditions on the specific features of the shear flow of viscous polymers in a confined two-dimensional channel with a wavy bottom is studied. The distribution of flow-rate disturbances across the transverse cross section of the channel is calculated by the numerical simulation of the Navier-Stokes equation for an incompressible fluid at arbitrary amplitudes and an arbitrary wave number of the wall. The wall slip is modeled by the introduction of a thin layer of a low-viscosity fluid at the bottom face. Slippage leads to a marked enhancement of flow rate disturbances including inertial advection. The results agree with the known analytical solutions for the low-amplitude wall wave.     

Rheometry-PIV of shear-thickening wormlike micelles

The shear-thickening behavior of an equimolar semidilute aqueous solution of 40 mM/L cetylpyridinium chloride and sodium salicylate was studied in this work by using a combined method of rheometry and particle image velocimetry (PIV). Experiments were conducted at 27.5 degrees C with Couette, vane-bob, and capillary rheometers in order to explore a wide shear stress range as well as the effect of boundary conditions and time of flow on the creation and destruction of shear-induced structures (SIS). The use of the combined method of capillary rheometry with PIV allowed the detection of fast spatial and temporal variations in the flow kinematics, which are related to the shear-thickening behavior and the dynamics of the SIS but are not distinguished by pure rheometrical measurements. A rich-in-details flow curve was found for this solution, which includes five different regimes. Namely, at very low shear rates a Newtonian behavior was found, followed by a shear thinning one in the second regime. In the third, shear banding was observed, which served as a precursor of the SIS and shear-thickening. The fourth and fifth regimes in the flow curve were separated by a spurtlike behavior, and they clearly evidenced the existence of shear-thickening accompanied by stick-slip oscillations at the wall of the rheometer, which subsequently produced variations in the shear rate under shear stress controlled flow. Such a stick-slip phenomenon prevailed up to the highest shear stresses used in this work and was reflected in asymmetric velocity profiles with spatial and temporal variations linked to the dynamics of creation and breakage of the SIS. The presence of apparent slip at the wall of the rheometer provides an energy release mechanism which leads to breakage of the SIS, followed by their further reformation during the stick part of the cycles. In addition, PIV measurements allowed the detection of apparent slip at the wall, as well as mechanical failures in the bulk of the fluid, which suggests an extra contribution of the shear stress field to the SIS dynamics. Increasing the residence time of the fluid in the flow system enhanced the shear-thickening behavior. Finally, the flow kinematics is described in detail and the true flow curve is obtained, which only partially fits into the scheme of existing theoretical models for shear-thickening solutions.     

Nonequilibrium molecular dynamics of the rheological and structural properties of linear and branched molecules. Simple shear and poiseuille flows; instabilities and slip

Nonequilibrium molecular-dynamics simulations are performed for linear and branched chain molecules to study their rheological and structural properties under simple shear and Poiseuille flows. Molecules are described by a spring-monomer model with a given intermolecular potential. The equations of motion are solved for shear and Poiseuille flows with Lees and Edward's [A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972)] periodic boundary conditions. A multiple time-scale algorithm extended to nonequilibrium situations is used as the integration method, and the simulations are performed at constant temperature using Nose-Hoover [S. Nose, J. Chem. Phys. 81, 511 (1984)] dynamics. In simple shear, molecules with flow-induced ellipsoidal shape, having significant segment concentrations along the gradient and neutral directions, exhibit substantial flow resistance. Linear molecules have larger zero-shear-rate viscosity than that of branched molecules, however, this behavior reverses as the shear rate is increased. The relaxation time of the molecules is associated with segment concentrations directed along the gradient and neutral directions, and hence it depends on structure and molecular weight. The results of this study are in qualitative agreement with other simulation studies and with experimental data. The pressure (Poiseuille) flow is induced by an external force F(e) simulated by confining the molecules in the region between surfaces which have attractive forces. Conditions at the boundary strongly influence the type of the slip flow predicted. A parabolic velocity profile with apparent slip on the wall is predicted under weakly attractive wall conditions, independent of molecular structure. In the case of strongly attractive walls, a layer of adhered molecules to the wall produces an abrupt distortion of the velocity profile which leads to slip between fluid layers with magnitude that depends on the molecular structure. Finally, the molecular deformation under flow depends on the attractive force of the wall, in such a way that molecules are highly deformed in the case of strong attracting walls.     

Analysis of electroosmotic flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.     

Viscoplastic flow and shear thickening in concentrated diblock copolymer solutions

Concentrated (typically 6%) solutions of a polystyrene-polyisoprene diblock copolymer in low viscosity paraffinic solvents form a micelle system by precipitating the polystyrene blocks, whereas the polyisoprene blocks are in solution. Besides viscoplastic behavior without thixotropy, this system exhibits a pronounced shear thickening in steady-state shear flow. The micelles are stable up to shear rates of more than 10⁵ s^–1. The properties of the solutions, especially the shear-thickening behavior, depend on the thermal history of the samples as well as on the solvent properties and are sensitive to flow field disturbances occurring in rotational viscometer devices with a profiled surface structure as commonly used to avoid wall slip in dispersed materials. The shear thickening is found to be related to the formation of a long-range ordered structure which also gives rise to the yield point. This long-range order enables aggregate flow with less energy dissipation at low shear rates. Shear-induced break-up of the aggregates appears as a shear-thickening transition which is observed in different types of flow fields.     

Yield stress of magnetic suspensions

The theories available for the yield stress of magnetic suspensions imply that their transition from a quasi-elastic to a fluid behavior is related to the disruption of chainlike or bulk columnlike aggregates connecting opposite boundaries of a region containing a suspension. It is commonly assumed that aggregates are rigidly bonded to bounding walls. However, a slip of aggregates on the walls is frequently observed. In this work, the transition from an elastic shear strain of a magnetic suspension to its viscous flow due to the slip of aggregates on channel walls is theoretically studied. The value of the corresponding yield stress is estimated.     

Hydrothermal stagnation point flow of Carreau nanofluid over a moving thin needle with non-linear Navier's slip and cubic autocatalytic chemical reactions in Darcy-Forchheimer medium

The present analysis deals with the hydrothermal and stagnation point flow of non-Newtonian fluid characterized by Carreau model over a moving thin needle. Darcy-Forchheimer medium is introduced. Homogeneous and heterogeneous chemical reactions are involved in the flow model. Non-linear Navier's slip condition is taken into account. Buongiorno model is adopted. The present hydrothermal flow model is useful in many complex industrial processes. The required numerical solution is obtained by 4th order Runge Kutta method along with shooting technique. The some remarkable outcomes of the current study are that axial velocity whittles down with rise in Weissenberg number and exhibits reverse trend in response to increase in non-linear slip parameter. Amplification of homogeneous and heterogeneous reaction parameters leads to diminution of nanoparticles concentration. Surface viscous drag intensify due to increment in Forchheimer number and heat transfer rate ameliorates with hike in Weissenberg number for both power law behavior (shear thinning and shear thickening) of Carreau nanofluid.     

Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography

In this work, expressions are constructed and solved that describe the velocity field of electroosmotic flow (EOF) in open tube capillary electrochromatography (CEC) systems when the possibility of having unequal tangential velocities at the liquid-solid interface is considered and a slip condition is employed as a boundary condition for the velocity of the EOF at the capillary wall. The coupled equations of hydrodynamics (momentum balance equation) and electrostatics (Poisson equation) are solved numerically in order to obtain the distribution of the velocity field as well as the value of the volumetric flow rate in the open tube. Also, expressions for the velocity field and the volumetric flow rate of the EOF are presented that are valid for certain electrolytic systems and for certain parameter values for which analytical solutions to the momentum balance and Poisson equations could be obtained. The results presented in this work indicate that having slip in the velocity of the EOF at the wall of the capillary could (i) substantially increase the electroosmotic velocity in the plug-flow region of the radial domain of the open capillary tube and (ii) increase the portion of the radial domain of the open capillary tube where the velocity of the EOF has a plug-flow profile, which in turn could increase the average velocity and volumetric flow rate of the EOF in the open capillary tube. Furthermore, the modeling approach and the results presented in this work indicate a method for experimentally evaluating the possibility of having slip in the velocity of the EOF at the capillary wall.     

Numerical Analysis of 3‐D Flow Past a Stationary Sphere with Slip Condition at Low and Moderate Reynolds Numbers

Computations are performed to determine the steady 3‐D viscous fluid flow forces acting on the stationary spherical suspended particle at low and moderate Reynolds numbers in the range of 0.1≤Re≤200. A slip is supposed on the boundary so that the slip velocity becomes proportional to the shear stress. This model possesses a single parameter to account for the slip coefficient λ (Pa.s/m), which is made dimensionless and is called Trostel number (Tr=λ a/μ). Decreasing slip, increases drag in all Reynolds limits, but slip has smaller effects on drag coefficient at lower Reynolds number regimes. Increasing slip at known Reynolds number causes to delay of flow separation and inflect point creation in velocity profiles. At full slip conditions, shear drag coefficient will be zero and radial drag coefficient reaches to its maximum values. Flow around of sphere at full‐slip condition is not equal to potential flow around a sphere. Present numerical results corresponding to full slip (Tr→0) are in complete accord with certain results of flow around of inviscid bubbles, and the results corresponding to no‐slip (Tr→∞) have excellent agreement with the results predicted by the no‐slip boundary condition.     

Effects of polymer adsorption on the effective viscosity in microchannel flows: phenomenological slip layer model from molecular simulations

Molecular simulations (Dissipative Particle Dynamics - DPD) were used to quantify the effect of polymer adsorption on the effective shear viscosity of a semi-dilute polymer solution in microchannel Poseuille flow. It is well known that polymer depletion layers develop adjacent to solid walls due to hydrodynamic forces, causing an apparent wall slip and reduced effective viscosity (increased total flow rate). We found that depletion layers also developed in the presence of hydrodynamically rough adsorbed layers on the wall. Polymer-polymer (steric) repulsion between flowing and adsorbed polymer expanded the depletion layer compared to no-adsorption cases, and the effective viscosity was reduced further. Desorption occurred for higher shear rates, reducing the repulsion effect and shrinking the depletion layers. A phenomenological algebraic model for the depletion layer thickness, including a shear modified adsorption isotherm, was developed based on the simulation data. The depletion layer model can be used together with the effective viscosity model we developed earlier.     

Hydrodynamics of interaction of particles (including cells) with surfaces

The study of the phenomena related to the motion of particles flowing in the proximity of the wall is pursued for purely cognitive reason as well as for some important practical purposes in various fields of technology, biology and medicine.When small spherical rigid particles move in the direction parallel to the surface their velocity is smaller than that of the fluid and depends on the ratio of the distance from the wall to the particle radius. The velocity of a particle falling down in a vertical cylinder is maximal in an eccentric position. A sphere in contact with the wall remains stationary. Translational velocity of spherical rigid particles the dimension of which are comparable to that of the tube is only slightly dependent of their lateral position. The differences in the flow parameters of deformable particles in comparison with rigid ones depend on the particle and fluid viscosity coefficient. When the particles move perpendicularly toward the wall, their velocity decreases as the particle approaches the surface. The change of particle velocity is inversely proportional to the gap.There are several theories explaining the influence of the channel diameter on the suspension viscosity (sigma phenomenon); a modern approach is based on the analysis of rheological properties of suspensions. The explanations of the Fahraeus effect (i.e. the fact that the concentration of particles flowing in a tube linking two containers are smaller than that in the containers) are based on non-uniform particle distribution in a transverse cross section and on the differences of velocities of particles and medium. The deviation of the velocity profile of a suspension of rigid particles flowing through a tube from the parabolic shape (blunting) does not depend on the flow velocity; as concerns deformable particles, however, this effect is the smaller the greater is the flow velocity.When the Reynolds number for particles is greater than 10^-3, there appears a component of particle velocity perpendicular to the streamline direction.This phenomenon is the cause of the lateral migration of particles. Neutrally buoyant rigid particles migrate to a certain concentrical region situated between the tube axis and the wall (tubular pinch region). Deformable neutrally buoyant particles migrate towards the tube axis, and deformable non-neutrally buoyant particles may move either toward the tube axis or toward the wall.In the research on the influence of the flow delimiting surface on the motion of particles in suspension a considerable progress has recently been made.However, the phenomena in this field are extremely complex. At present, two main types of approach may be distinguished. On a microscopic level direct interactions between particles and surfaces are analyzed. A macroscopic approach consists in treating particle suspension as fluid, and overall influence of the surface on its properties are studied. A comprehensive theory linking these two levels has not yet emerged.     

Flocculated flow of microfibrillated cellulose water suspensions: an imaging approach for characterisation of rheological behaviour

Our aim was to characterise the suspension rheology of microfibrillated cellulose (MFC) in relation to flocculation of the cellulose fibrils. Measurements were carried out using a rotational rheometer and a transparent cylindrical measuring system that allows combining visual information to rheological parameters. The photographs were analyzed for their floc size distribution. Conclusions were drawn by comparing the photographs and data obtained from measurements. Variables selected for examination of MFC suspensions were degree of disintegration of fibres into microfibrils, the gap between the cylinders, sodium chloride concentration, and the effects of changing shear rate during the measurement. We studied changes in floc size under different conditions and during network structure decomposition. At rest, the suspension consisted of flocs sintered together into a network. With shearing, the network separated first into chain-like floc formations and, upon further shear rate increase, into individual spherical flocs. The size of these spherical flocs was inversely proportional to the shear rate. Investigations also confirmed that floc size depends on the geometry gap, and it affects the measured shear stress. Furthermore, suspension photographs revealed an increasing tendency to aggregation and wall depletion with sodium chloride concentration of 10⁻³ M and higher.