Volume 51, Issue 1, January 2007
Index of content:
Monodomain dynamics for rigid rod and platelet suspensions in strongly coupled coplanar linear flow and magnetic fields51(2007); http://dx.doi.org/10.1122/1.2400704View Description Hide Description
Extensional flows and magnetic fields induce similar steady alignment responses when applied to liquid crystals(LCs),liquid crystal polymers(LCPs) and nematic (rigid rod or platelet) suspensions. This observation is explained for LCs by a classical analogy, expressed as a symmetry, between hydrodynamic and magnetic fields in the Leslie-Ericksen theory [de Gennes and Prost, The Physics of Liquid Crystals (Oxford University Press, New York, 1993); Chandrasekhar, Liquid Crystals (Cambridge University Press, London, 1992)]. Our purpose here is to extend this analogy: first, to LCPs and nematic suspensions where an excluded volume potential couples either to a linear flow [Hess, Z. Naturforsch. A31a, 1034–1037 (1976); Doi and Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] or to a magnetic field [Bhandar and Wiest, J. Colloid Interface Sci.257, 371–382 (2003)]; and second, to the strong coupling of excluded volume interactions, planar linear flows, and a coplanar magnetic field. The general symmetries reveal parameter redundancies in the Doi-Hess kinetic theory, leading to a reduced model with significant computational savings. That is, a rotational planar linear LCP (or nematic suspension)flow under an imposed coplanar magnetic field is reducible to a simple shear flow coupled with a transversely imposed magnetic field and negative anisotropy through an orthogonal transformation; whereas a magnetic field coupled linear, irrotational flow corresponds to a tri-directional elongation. We illustrate these results with a second-moment tensor model to predict how a variable strength, coplanar magnetic field may be used to alter or control flow-induced responses of LCPs or nematic suspensions. The illustrations are for sheared dynamic attractors (tumbling, kayaking and chaotic), extension-induced steady states, and four roll mill flows.
51(2007); http://dx.doi.org/10.1122/1.2360670View Description Hide Description
Our previous, extensively validated, nonlinear viscoelastic formalism for glassy polymers is extended to include the effects of chemical reaction. Two modifications are necessary. First, the extent of reaction represents an additional degree of freedom that must be included in the free energy series expansion. Second, simultaneous reaction and deformation can lead to “compression set” that is represented by an evolving stress-free configuration in the cross-linked solid. The material clock, which is based on potential energy and must also incorporate these modifications, naturally predicts the increase in glass transition with cure.
Experimental investigation and phenomenological modeling of the viscosity-shear rate of bimodal high solid content latex51(2007); http://dx.doi.org/10.1122/1.2391069View Description Hide Description
The nonlinear rheological behavior of different monomodal and bimodal polystyrene model latices has been investigated. The objective of the present work is to develop a practical approach for the modeling of the evolution of the viscosity of bimodal latices based only on the experimental behavior of related monomodal components. For this purpose, the viscosity curve of monomodal latices is described using the Carreau–Yasuda in order to obtain a phenomenological depiction of the shear thinning behavior. Following this, the Carreau–Yasuda law was extended to describe the complex viscosity behavior of bimodal latices. The parameters of the Carreau–Yasuda model, i.e., the zero shear viscosity, the high shear viscosity, and the inverse of the onset of shear-thinning are expressed from the Krieger–Dougherty equation. The extension of the Krieger–Dougherty equation to bimodal latices is based on the porosity model developed by Ouchiyama and Tanaka [Ind. Eng. Chem. Fundam.23, 490–493 (1984)], and used to calculate the variations of parameters , , and versus the volume fraction of particles for bimodal latices. This modeling approach developed in this manner shows that the complex viscosity behavior of concentrated and bimodal latices can be derived from the rheological behavior of monomodal components, which is an extremely useful development from the point of view of process engineering applications. In addition, the phenomenon of shear-thickening behavior of polydisperse concentrated latices is also investigated.
51(2007); http://dx.doi.org/10.1122/1.2399084View Description Hide Description
We study the dynamics of elongated axisymmetric particles undergoing shear flow between two parallel planar walls, under creeping-flow conditions. Particles are modeled as linear chains of touching spheres and it is assumed that walls are separated by a distance comparable to particle length. The hydrodynamic interactions of the chains with the walls are evaluated using our Cartesian-representation algorithm [Bhattacharya et al., Physica A356, 294–340(2005b)]. We find that when particles are far from both walls in a weakly confined system, their trajectories are qualitatively similar to Jeffery orbits in unbounded space. In particular, the periods of the orbits and the evolution of the azimuthal angle in the flow-gradient plane are nearly independent of the initial orientation of the particle. For stronger confinements, however, (i.e., when the particle is close to one or both walls) a significant dependence of the angular evolution on the initial particle configuration is observed. The phases of particle trajectories in a confined dilute suspension subject to a sudden onset of shear flow are thus slowly randomized due to unequal trajectory periods, even in the absence of interparticle hydrodynamic interactions. Therefore, stress oscillations associated with initially coherent particle motions decay with time. The effect of near contact particle-wall interactions on the suspension behavior is also discussed.
Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear51(2007); http://dx.doi.org/10.1122/1.2399088View Description Hide Description
We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the dissipative stress tensor must be similar to that of nematics/smectics but with the local variable being the slowly varying lamellar wave vector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicularly oriented lamellae in a uniform, oscillatory, shear flow, and show that the configuration can be hydrodynamically unstable for the constitutive law chosen. It is argued that this instability and the secondary flows it creates can be used to infer a possible mechanism for orientation selection in shear experiments.
51(2007); http://dx.doi.org/10.1122/1.2401614View Description Hide Description
We have studied the motion of spheres falling through yield-stress Carbopol gels. We measured the velocity of the falling sphere as a function of time and sphere density. Reproducible results were obtained when the experimental fluids were carefully prepared and homogenized. Three regimes of motion were observed. Spheres of high enough density reached a constant terminal velocity, as in Newtonian fluids. Below a critical density, the sphere came to a complete stop, while in an intermediate regime, the sphere continued to move but with a velocity which steadily decreased with time. We have also carefully characterized the rheological behavior of the fluids. The flow regimes observed for the falling sphere are analogous to those observed in creep tests for different applied stress levels. The yielding criterion and the drag force on the sphere obtained from our data are in excellent agreement with the longstanding but previously unconfirmed theoretical predictions of Beris et al. [J. Fluid Mech.158, 219–244 (1985)] and Beaulne and Mitsoulis [J. Non-Newtonian Fluid Mech.72, 55–71 (1997)].
51(2007); http://dx.doi.org/10.1122/1.2399089View Description Hide Description
The effect of geometrical confinement on the deformation and orientation of single droplets during steady-state shear flow is investigated microscopically in a counterrotating device. The model system consists of poly(dimethyl siloxane) droplets of varying sizes and viscosities in a poly(isobutylene) matrix. The experimental results are first compared with the predictions of the model by Maffettone and Minale [J. Non-Newtonian Fluid Mech.78, 227–241 (1998)] for bulk flow. For all viscosity ratios, deviations from the Maffettone and Minale model start to occur at a droplet diameter to gap spacing ratio of the order of 0.4. The dropletdeformation increases and the droplets orient more towards the flow direction as a consequence of confinement. At low viscosity ratios, the deviations remain small, whereas at high viscosity ratios, larger deviations from bulk behavior are observed. The observations are also compared with the theory of Shapira and Haber [Int. J. Multiphase Flow16, 305–321 (1990)] which includes the influence of wall effects on deformation. The Shapira and Haber model is modified by replacing the Taylor model as bulk reference by the Maffettone and Minale model. Good agreement between theory and experimental results is found for a wide range of viscosity ratios.