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.
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.
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.
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 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.
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).
The rheological properties of methylcellulose in N,N-dimethylformamide (MC-DMF) gel are investigated to prepare extruded beads. The temperature scan under dynamic compression for various concentrations of MC in DMF is performed to investigate the rapture of MC gel at a constant frequency of 1 Hz. The morphological studies are performed using a scanning electron microscope (SEM) to analyze the size and shape of dried bead. However, during swelling studies, the MC beads have the capability to swell and retain a large amount of water >?9150% by weight and 9192.6% by volume. The mechanism of swelling is thermodynamically verified, where the enthalpy of hydration of initial layer of MC bead is negative. The newly defined electrostatic penta-pole model explains the anomalous behavior of urea release, where urea is assumed to be electrostatically bounded with the MC molecules.
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.
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.
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.
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.
First, we obtain necessary and sufficient conditions for the complete integrability and linearizability of this system. Then, we discuss the problem of existence of one first integral of the form \(\psi ^{(1)}(x,y,z)=xy+O(|x,y,z|^3)\). Computation of resonant focus quantities and the decomposition of the variety of the ideal that they generate in the ring of polynomials of parameters \(a_{ij},b_{ij},c_{ij}\) of the system were used to obtain necessary conditions of integrability and linearizability. The theory of Darboux integrability and some other methods are used to show the sufficiency. In the investigation of the conditions for the existence of one first integral the decomposition of the variety mentioned above was performed using modular computations, its consequences are discussed.
The fundamental assumption of the paper is that the extra stress tensor of an electrorheological fluid is an isotropic tensor valued function of the rate of strain tensor D and the vector n (which characterizes the orientation
and length N of the fibers formed by application of an electric field). The resulting constitutive equation for is supplemented by the solution of the previously studied time evolution equation for n. Plastic behavior for the shear and normal stresses is predicted. Anticipating that the action of increasing shear rate
is i) to orient the fibers more and more in the direction of flow and ii) simultaneously to break up the fibers leads to the conclusion that for
the same behavior is encountered as without an electric field. Using realistically possible approximation formulas for the dependence of
and N on
leads to the Bingham behavior for
and power law behavior for large shear rates.
where \(g \in {\mathcal {C}}^1({\mathbb {R}})\) is a bounded function of constant sign, \(a^+,a^-: [0,T] \rightarrow {\mathbb {R}}^+\) are the positive/negative part of a sign-changing weight \(a(t)\) and \(\mu > 0\) is a real parameter. Depending on the sign of \(g^{\prime }(u)\) at infinity, we find existence/multiplicity of solutions for \(\mu \) in a “small” interval near the value
The proof exploits a change of variables, transforming the sign-indefinite Eq. (1) into a forced perturbation of an autonomous planar system, and a shooting argument. Nonexistence results for \(\mu \rightarrow 0^+\) and \(\mu \rightarrow +\infty \) are given, as well.
