This paper proposes a mechanical measurement technique of the planar elongation viscosity of the low-viscosity liquids. A newly designed flow cell, which consists of a cylindrical cup and a disk-shaped bob with a knife-edged rim, generates the planar elongation flow. Three kinds of Newtonian fluids and an M1 fluid are used. A strain control rheometer pushed the bob into the cup filled with the test fluid and measured the resistant force. The planar elongation viscosity was evaluated using the following two assumptions: first, the resistant force is regarded as the sum of the buoyancy and the resultant forces caused by pressure drops in the planar elongation flow and the shear flow in the test section. Second, the hydraulic mean depth is used as a representative length. The relative errors of the Trouton ratio of the Newtonian fluids were less than 20% compared to the theoretical value of 4.
We investigate the electrorheological (ER) properties of clay (montmorillonite, sepiolite, and laponite®). The selected clays allow to distinguish between planar particles of different sizes (montmorillonite and laponite®), and elongated ones (sepiolite). The effect of coating them with the surfactant CTAB improves dispersibility in the oil medium and favors the ER response, prticularly in the case of laponite®, whereas in the case of montmorillonite, microscopic observations show that the columnar structures are broken in places leading to a reduced yield stress. Both the static yield stress and the storage modulus grow faster with the field in sepiolite suspensions as compared to laponite®. When dealing with mixed systems, it is found that the field-induced montmorillonite structures are reinforced by the addition of either laponite® or sepiolite, whereas when the latter two are combined, it is laponite® that dominates the ER response.
Entanglement network of carboxymethyl cellulose (CMC) was characterized based on the dynamic viscoelasticity of the concentrated solutions in an ionic liquid. According to the concentration dependence of the molecular weight between entanglements (Me), Me for the molten state (Me,melt) for CMC was estimated to be 3.9 × 103 as a chain variable reflecting the chemical structure of the polysaccharide. Furthermore, relations between Me,melt and other chain variables were examined to elucidate the specificity in the entanglement properties of CMC and related polysaccharides. It was shown that the number of entanglement strands (Pe), the ratio of the cube of the tube diameter, and the volume occupied by the entanglement strand, for CMC was 72 being significantly larger than the universal value of ca. 20 recognized for flexible polymers. Anomalous values of Pe > 20 were also obtained for related polysaccharides such as cellulose and amylose.
A numerical approach based on Tikhonov regularization is developed to invert torque curves from time-dependent small amplitude oscillatory shear (SAOS) experiments in which diffusion occurs to determine the diffusion coefficient. Diffusion of a solvent into a polymer melt for example causes the measured torque to decrease over time and is thus dependent on diffusion kinetics and the concentration profile. Our numerical approach provides a general method for retrieving local viscosity profiles during diffusion with reasonable accuracy, depending only on the linear viscoelastic constitutive equation and a general power law dependency of the diffusion process on time. This approach also allows us to identify the type of diffusion (Fickian, pseudo-Fickian, anomalous, and glassy) and estimate the diffusion coefficient without the a priori identification of a specific diffusion model. Retrieving local viscosity profiles from torque measurements in the presence of a concentration gradient is an ill-posed problem of the second type and requires Tikhonov regularization. The robustness of our approach is demonstrated using a number of virtual experiments, with data sets from Fickian and non-Fickian theoretical concentration and torque profiles as well as real experimental data.
The role of friction in non-colloidal suspensions is examined with a model which splits the viscosity into a frictionless component (τ*) plus a frictional component which depends on the ratio of the particle pressure (P) to the shear stress (τ). The model needs the input by computation of τ* and P and a suitable choice of particle friction coefficient (μ). It can be extended to elongational flows and cases where sphere roughness is important; volume fractions up to 0.5 are considered. It is shown that friction acts in a feedback or “bootstrap” manner to increase the suspension viscosity. The analysis is also useful for deducing the friction coefficient in suspensions from experimental data. It was applied to several sets of experimental data and reasonable correlations of the viscosities were demonstrated. An example of the correlation for spheres in a silicone oil is shown for volume fractions 0.1–0.5.
This work presents different rheological methods to determine the effect of fiber surface treatment on their interaction with a polymer matrix. In particular, surface-initiated catalytic polymerization was investigated on hemp fibers to improve their adhesion with linear medium-density polyethylene (LMDPE). The selected rheological tests (creep-recovery (solid state), small and large amplitude oscillation shear, and transient rheology (melt state)) were used to compare the treated and untreated fiber composites with the neat matrix. The results showed a significant improvement of the treated hemp composite (LPHC) creep modulus with respect to its untreated counterpart (LNHC) leading to a reduction of the creep strain, especially as temperature increases. The transient viscosity was modeled using a modified Kohlrausch-Williams-Watt (KWW) equation showing an increase in the transient viscosity (\( {\eta}_0^{+} \)) and relaxation time (τ) with fiber addition and surface treatment. These results were confirmed by large amplitude oscillatory shear (LAOS) through the reduction of the relative third harmonic (I3/1), intrinsic nonlinearity parameter (Q0), and nonlinear viscoelastic ratio (NRL). The results clearly show that catalytic polymerization is a good surface modification technique to increase the compatibility between natural fibers and polymer matrices as to improve all their final properties.
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.
Fibrin promotes wound healing by serving as provisional extracellular matrix for fibroblasts that realign and degrade fibrin fibers, and sense and respond to surrounding substrate in a mechanical-feedback loop. We aimed to study mechanical adaptation of fibrin networks due to cell-generated forces at the micron-scale. Fibroblasts were elongated-shaped in networks with ≤?2 mg/ml fibrinogen, or cobblestone-shaped with 3 mg/ml fibrinogen at 24 h. At frequencies f?<?102 Hz, G′ of fibroblast-seeded fibrin networks with ≥?1 mg/ml fibrinogen increased compared to that of fibrin networks. At frequencies f?>?103 Hz, G″ of fibrin networks decreased with increasing concentration following the power-law in frequency with exponents ranging from 0.75?±?0.03 to 0.43?±?0.03 at 3 h, and of fibroblast-seeded fibrin networks with exponents ranging from 0.56?±?0.08 to 0.28?±?0.06. In conclusion, fibroblasts actively contributed to a change in viscoelastic properties of fibrin networks at the micron-scale, suggesting that the cells and fibrin network mechanically interact. This provides better understanding of, e.g., cellular migration in wound healing.
The Herschel–Bulkley rheological parameters of an environmentally friendly drilling fluid formulated based on an Algerian bentonite and two polymers—hydroxyethyl cellulose and polyethylene glycol—have been optimized using a genetic algorithm. The effect of hydroxyethyl cellulose, temperature, pH and sodium chloride (NaCl) on the three-parameter Herschel-Bulkley model was also studied. The genetic algorithm technique provided improved rheological parameter characterization compared to the nonlinear regression, especially in the case of drilling fluids formulated with sodium chloride making it a better choice. Furthermore, the oscillatory test offered more reliable yield stress values. The rheological parameters were found to be very sensitive to different conditions. Yield stress and consistency index increased with increasing the hydroxyethyl cellulose concentration, reaching maximum at a temperature of 65 °C and decreased with decreasing pH and also when adding sodium chloride to the drilling fluid. The flow index changed inversely to yield stress and consistency index. The physical origins of these changes in rheological parameters were discussed and correlation between variation in rheological parameters and bentonite suspension properties were concluded. Based on these results, it is recommended to use the proposed formulation of drilling fluid at high temperature and when the formation of alkaline pH is encountered due to the gelation mechanism and to select the optimum concentration of NaCl to avoid degradation of the rheological parameters.
Complex rheological trends of several commercially available and lab-made prototype toothpastes are reported. The flow curves are generated using the rotational rheometers with a series of rheological procedures, comprising of stress ramps, creep-recovery, stepped-shear rates, and dynamic oscillatory strain sweeps performed on toothpastes. Intricacies due to the history and the effects of pre-conditioning of the samples are discussed. However, the main goal of this work was to identify the correlations between the rheological measurements and the consumer-perceived properties of toothpastes. Shape retention and stringiness are the main sensory properties of interest that were identified and evaluated by the panelists. A custom-built experimental setup is used to quantify shape retention of a toothpaste ribbon on a brush and on a flat surface in a test which resonates with the popular slump test. It is demonstrated that the degree of shape retention correlates with the yield stress and the instantaneous viscosity. A comparison of yield stresses obtained using different methods in relation to degree of shape retention is presented. An experimental setup designed to measure stringiness of toothpastes is delineated. The stringiness measured with this device correlates well with human perception and also with the slope of the flow curve, i.e., the higher the degree of shear thinning, the less stringy the pastes tend to be. For lab-made prototype toothpastes, basic structure-property relations are established in terms of correlations between the three formulation variables: thickening silica, Xanthan gum, and carboxymethyl cellulose (CMC).
We propose a simple, robust method to measure both the first and second normal stress differences of polymers, hence obtaining the full set of viscometric material functions in nonlinear shear flow. The method is based on the use of a modular cone-partitioned plate (CPP) setup with two different diameters of the inner plate, mounted on a rotational strain-controlled rheometer. The use of CPP allows extending the measured range of shear rates without edge fracture problems. The main advantage of such a protocol is that it overcomes limitations of previous approaches based on CPP (moderate temperatures not exceeding 120 °C, multiple measurements of samples with different volume) and yields data over a wide temperature range by performing a two-step measurement on two different samples with the same volume. The method was tested with two entangled polystyrene solutions at elevated temperatures, and the results were favorably compared with both the limited literature data on the second normal stress difference and the predictions obtained with a recent tube-based model of entangled polymers accounting for shear flow-induced molecular tumbling. Limitations and possible improvements of the proposed simple experimental protocol are also discussed.
Graphical abstract The effects of edge fracture in start-up shear experiments can be circumvented with the use of a cone-partitioned plate (CPP) geometry. Such a device consists of an inner measuring plate surrounded by an outer nonmeasuring corona. The radius of the sample exceeds that of the measuring plate so that the measured volume is not affected by edge instability. However, the measured first normal stress difference is an apparent one (Napp,1), owing to the contribution of the nonmeasured part of the sample. The figure depicts a schematic design of a modular CPP geometry. Such a fixture is built in a way that the inner tool and the outer partition can be easily replaced, in order to have different measuring diameters (i.e., 6 and 10 mm). From the corresponding signals of the Napp,1, the effective first and second normal stress differences can be calculated.
Concentrated solutions of nearly monodisperse poly(methyl methacrylate), PMMA-270k and PMMA-86k, in oligo(methyl methacrylate), MMA o-4k and MMA o-2k, investigated by Wingstrand et al. (Phys Rev Lett 115:078302, 2015) and Wingstrand (2015) do not follow the linear-viscoelastic scaling relations of monodisperse polystyrenes (PS) dissolved in oligomeric styrene (Wagner in Rheol Acta 53:765–777, 2014a, in Non-Newtonian Fluid Mech 222:121–131, 2014b; Wagner et al. in J Rheol 59:1113–1130, 2015). Rather, PMMA-270k shows an attractive interaction with MMA, in contrast to the interaction of PMMA-86k and MMA. This different behavior can be traced back to different tacticities of the two polymers. The attractive interaction of PMMA-270k with o-4k creates pseudo entanglements, which increase the interchain tube pressure, and therefore, the solution PMMA-270k/o-4k shows, as reported by Wingstrand et al. (Phys Rev Lett 115:078302, 2015), qualitatively a similar scaling of the elongational viscosity with \( {\left(\dot{\varepsilon}{\tau}_R\right)}^{-1/2} \) as observed for polystyrene melts. For the solution PMMA-270/o-2k, this effect is only seen at the highest elongation rates investigated. The elongational viscosity of PMMA-86k dissolved in oligomeric MMA is determined by the Rouse time of the melt, as in the case of polystyrene solutions.
The uptake of proteins is highly recommended, mainly for athletes, elderly people and patients with serious diseases like dysphagia. In this work, whey proteins were used for producing two kinds of aqueous materials: suspensions of proteins, in the native form, and gels, obtained by protein denaturation. In the first system, proteins are used as interfacial active ingredients or as thickening agents of the aqueous phase, whereas in the second one they are used as structuring agents. These protein-based materials show very different rheological and microstructural behaviour even at the same concentration. In the case of an undenatured system, a growing protein fraction resulted in an increased dimension of their aggregates and all investigated systems exhibited a liquid-like behaviour with a viscosity independent of shear rate and well described by a Krieger-Dougherty model. In the case of thermally denatured systems, it has been observed that, at increasing protein content, aggregates evolve towards a continuous gel network with a fractal behaviour. Both systems have been modelled, according to their specific behaviour, with the aim of proposing equations suitable to relate macroscopic properties and microstructure, useful for designing new food products with predictable properties for different industrial uses.
Dense colloidal suspensions are processed in a wide variety of industries. Challenges for pumping suspensions and slurries at high concentrations include shear thickening and dilation, which can have deleterious consequences. These systems are shear sensitive close to the jamming point, meaning that a significant increase in high shear viscosity can be observed with just a few percent change in volume fractions. Therefore, accurate and rapid determination of the jamming point can greatly aid formulation. Typically, conventional rheometry identifies the jamming point by a time-consuming process, whereby multiple flow curves of suspensions of different volume fraction are measured and extrapolated to the volume fraction where the viscosity diverges. We present an alternative approach for rapid, one-step, experimental determination of the jamming point for aqueous suspensions. The procedure monitors the shear stress under constant shear stress or shear rate as the sample is dewatered using immobilization cell rheometry, until the viscosity diverges. The method is validated by comparing the results of this work with conventional rheometry for a model suspension. Then it is applied to examine the effect of grafting a short-chain polymer to particles, comprising an industrial suspension of silica-coated titania. Polymeric coating of the particles increases the jamming concentration and mitigates shear thickening, qualitatively consistent with predictions from simulations.
A new method is designed to extract the jamming point of a suspension. The procedure monitors the effective viscosity under prescribed shear conditions as the suspension is dewatered using immobilization cell rheometry. The geometry moves down to accommodate solvent evaporation, until the viscosity diverges, and the jamming point is reached.
under Dirichlet boundary condition, where \(p>2\) and \(f:[0,l]\times {\mathbb {R}}\rightarrow {\mathbb {R}}\) is a continuous function with \(f(x,0)=0\). We will prove that if there is at least one eigenvalue of the p-Laplace operator between \(\lim _{u\rightarrow 0} f(x,u)/|u|^{p-2}u\) and \(\lim _{|u|\rightarrow +\infty } f(x,u)/|u|^{p-2}u\), then there exists a nontrivial stationary solution. Moreover we show the existence of a connecting orbit between stationary solutions. The results are based on Conley index and detect stationary states even when those based on fixed point theory do not apply. In order to compute the Conley index for nonlinear semiflows deformation along p is used.
In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution \((0.9~\upmu \hbox {m})\). Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of \(400\times 400\times 150\,\upmu \hbox {m}^{3}\) and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure–saturation Open image in new window imbibition curves for various domain sizes. We studied the directional dependence of Open image in new window curves by simulating water penetration into the layer from various directions. We did not find any significant difference between Open image in new window curves in different directions. We studied the effect of compression of paper on Open image in new window curves. We found that up to 30% compression of the paper layer had very small effect on the Open image in new window curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them. 相似文献
We investigate experimentally the effect of aspect ratio ( ) on the time-varying, three-dimensional flow structure of flat-plate wings rotating from rest at 45° angle of attack. Plates of = 2 and 4 are tested in a 50 % by mass glycerin–water mixture, with a total rotation of ? = 120° and a matched tip Reynolds number of 5,000. The time-varying, three-component volumetric velocity field is reconstructed using phase-locked, phase-averaged stereoscopic digital particle image velocimetry in multiple, closely-spaced chordwise planes. The vortex structure is analyzed using the $\mathcal{Q}$-criterion, helicity density, and spanwise quantities. For both s, the flow initially consists of a connected and coherent leading-edge vortex (LEV), tip vortex (TV), and trailing-edge vortex (TEV) loop; the LEV increases in size with span and tilts aft. Smaller, discrete vortices are present in the separated shear layers at the trailing and tip edges, which wrap around the primary TEV and TV. After about ? = 20°, the outboard-span LEV lifts off the plate and becomes arch-like. A second, smaller LEV and the formation of corner vortex structures follow. For = 4, the outboard LEV moves farther aft, multiple LEVs form ahead of it, and after about ? = 50° a breakdown of the lifted-off LEV and the TV occurs. However, for = 2, the outboard LEV lift-off is not progressive, and the overall LEV-TV flow remains more coherent and closer to the plate, with evidence of breakdown late in the motion. Inboard of about 50 % span, the = 4 LEV is stable for the motion duration. Up to approximately 60 % span, the = 2 LEV is distinct from the TV and is similarly stable. The = 2 LEV exhibits substantially higher spanwise vorticity and velocity. The latter possesses a “four-lobed” distribution at the periphery of the LEV core having adjacent positive (outboard) and negative (inboard) components, corresponding to a helical streamline structure. Both s show substantial root-to-tip velocity aft of the stable LEV, which drives outboard spanwise vorticity flux; flux toward the root is also present in the front portion of the LEV. For = 2, there is a strong flux of spanwise vorticity from the outboard LEV to the tip, which may mitigate LEV lift-off and is not found for = 4. The TV circulation for each is similar in magnitude and growth when plotted versus the chord lengths travelled by the tip, prior to breakdown. Streamwise vorticity due to the TV induces high spanwise velocity, and for = 2, the tilted LEV creates further streamwise vorticity which corresponds well to spanwise-elongated regions of spanwise velocity. For = 2, the TV influences a relatively greater portion of the span and is more coherent at later times, which coupled with the tilted LEV strongly contributes to the higher overall spanwise velocity and vorticity flux. 相似文献
