Flow Gradient Direction Research Articles

Bulk and interfacial modes of instability in channel flow of thixotropic-viscoelasto-plastic fluids with shear-banding

We carry out a linear stability analysis of the generalised BMP model, which incorporates the shear-banding phenomenon into flows of thixotropic-viscoelasto-plastic fluids: common behaviours observed in wormlike micellar solutions. We introduce a new dimensionless parameter governing shear-banding, and find that when a flow is unstable in the absence of shear-banding, this parameter has a stabilising effect. Above a critical value of the shear-banding parameter, shear bands appear in the flow gradient direction. Here two different modes of instability are observed: a bulk mode (which is the same as that seen in the absence of shear banding) and an interfacial mode. We found that the former dominates over the latter at low values of the shear-banding parameter, but the interfacial instability becomes dominant at very high values of the parameter. In particular, the interfacial modes are more unstable in flows where the low shear band has almost constant viscosity. The two modes of instability depend on different material timescales: interfacial modes become more dangerous if the interface location is near the channel wall, which is seen when the structural relaxation time is much larger than that of plasticity, while bulk modes (as seen in previous work) are highly unstable if the timescale of viscoelasticity is much longer than both those of plasticity and thixotropy.

Edge fracture instability in sheared complex fluids: Onset criterion and possible mitigation strategy

We perform a detailed theoretical study of the edge fracture instability, which commonly destabilizes the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson–Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on the shear rate of the shear and normal stresses. The threshold for the onset of edge fracture is shown to be relatively robust against variations in the wetting angle where the fluid-air interface meets the hard walls of the flow cell, whereas the nonlinear dynamics depend strongly on the wetting angle. We perform a linear stability calculation to derive an exact analytical expression for the onset of edge fracture, expressed in terms of the shear-rate derivative of the second normal stress difference, the shear-rate derivative of the shear stress (sometimes called the tangent viscosity), the jump in the shear stress across the interface between the fluid and the outside air, the surface tension of that interface, and the rheometer gap size. (The shear stress to which we refer is σxy with x^ being the flow direction and y^ being the flow-gradient direction. The interface normal is in the vorticity direction z^.) Full agreement between our analytical calculation and nonlinear simulations is demonstrated. We also elucidate in detail the mechanism of edge fracture and finally suggest a new way in which it might be mitigated in experimental practice. We also suggest that, by containing the second normal stress difference, our criterion for the onset of edge fracture may be used as a means to determine that quantity experimentally. Some of the results in this paper were first announced in an earlier letter [E. J. Hemingway, H. Kusumaatmaja, and S. M. Fielding, Phys. Rev. Lett. 119, 028006 (2017)]. The present paper provides additional simulation results, calculational details of the linear stability analysis, and more detailed discussion of the significance and limitations of our findings.

Short-Term Flow Induced Crystallization in Isotactic Polypropylene: How Short Is Short?

The so-called “short-term flow” protocol is widely applied in experimental flow-induced crystallization studies on polymers in order to separate the nucleation and subsequent growth processes [Liedauer et al. Int. Polym. Proc. 1993, 8, 236–244]. The basis of this protocol is the assumption that structure development during flow can be minimized and the rheological behavior, i.e., the viscosity, does not change noticeably. In this work we explore the validity of this assumption for short but strong flows and reveal the structure formation during the early stages of crystallization. Viscosity and structure evolution of an isotactic polypropylene (iPP, Mw ≈ 365 kg/mol and Mw/Mn = 5.4) melt at 145 °C are measured during the short-flow period (0.2–0.25 s) using the combination of a slit rheometer and fast X-ray scattering measurements. For high enough (apparent) shear rates (≥240 s–1) a viscosity rise during flow is observed; i.e., the condition for “short-term flow” is not satisfied. With a time delay with respect to the viscosity rise, the development of shish is observed at a position halfway the length of slit, along the flow direction, by means of ultrafast time-resolved SAXS measurements. Depending on the shear rate, these shish are detected during (shear rates ≥ 400 s–1) or after flow (240 s–1 ≤ shear rates < 400 s–1). For even lower shear rates of 160 and 80 s–1, the viscosity does not change significantly, and instead of shish, oriented row nuclei (X-ray undetectable) are generated. These two shear conditions qualify as short-term flow. A full understanding of the coupled flow and crystallization phenomena requires that the transient and nonhomogeneous behaviors, both in flow and in flow gradient direction, have to be taken into account. This can only be done by a full numerical model, and therefore, the results presented in this paper also provide a valuable data set for future numerical studies.

Rheology of cubic blue phases

We study the behaviour of cubic blue phases under shear flow via lattice Boltzmann simulations. We focus on the two experimentally observed phases, Blue Phase I (BPI) and Blue Phase II (BPII). The disclination network of Blue Phase II continuously breaks and reforms under steady shear, leading to an oscillatory stress response in time. For larger shear rates, the structure breaks up into a Grandjean texture with a cholesteric helix lying along the flow gradient direction. Blue Phase I leads to a very different response. Here, oscillations are only possible for intermediate shear rates -- very slow flow causes a transition of the initially ordered structure into an amorphous network with an apparent yield stress. Larger shear rates lead to another amorphous state with different structure of the defect network. For even larger flow rates the same break-up into a Grandjean texture as for Blue Phase II is observed. At the highest imposed flow rates both cubic blue phases adopt a flow-aligned nematic state. Our results provide the first theoretical investigation of sheared blue phases in large systems, and are relevant to understanding the bulk rheology of these materials.

Structure scaling properties of confined nematic polymers in plane Couette cells: The weak flow limit

One of the confounding issues in laminar flow processing of nematic polymers is the generation of molecular orientational structures on length scales that remain poorly characterized with respect to molecular and processing control parameters. For plane Couette flow within the Leslie–Ericksen continuum model, theoretical results since the 1970s yield two fundamental predictions about the length scales of nematic distortion: a power law scaling behavior, Er−p, 14⩽p⩽1, where Er is the Ericksen number (ratio of viscous to elastic stresses); the exponent p varies according to whether the structure is a localized boundary layer or an extended structure. Until now, comparable results which incorporate molecular elasticity (i.e., distortions in the shape of the orientational distribution) have not been derived from mesoscopic Doi–Marrucci–Greco (DMG) tensor models. In this paper, we derive asymptotic, one-dimensional gap structures, along the flow-gradient direction, in “slow” Couette cells, which reflect self-consistent coupling between the primary flow, in-plane director (nematic) and order parameter (molecular) elasticity, and confinement conditions (plate speeds, gap height, and director anchoring angle). We then read off the small Deborah number, viscoelastic structure predictions: The flow is simple shear. The orientation structures consist of: two molecular-elasticity boundary layers with the Marrucci scaling Er−1/2, which are amplified by tilted plate anchoring; and a nonuniform, director-dominated structure that spans the entire gap, with Er−1 average length scale, present for any anchoring angle. We close with direct numerical simulations of the DMG steady, flow-nematic boundary-value problem, first to benchmark the small Deborah number structure formulas, and then to document onset of new flow-orientation structures as the asymptotic expansions become disordered.

Shear- and magnetic-field-induced ordering in magnetic nanoparticle dispersion from small-angle neutron scattering.

Small-angle neutron scattering experiments have been performed to investigate orientational ordering of a dispersion of rod-shaped ferromagnetic nanoparticles under the influence of shear flow and static magnetic field. In this experiment, the flow and flow gradient directions are perpendicular to the direction of the applied magnetic field. The scattering intensity is isotropic in zero-shear-rate or zero-applied-field conditions, indicating that the particles are randomly oriented. Anisotropic scattering is observed both in a shear flow and in a static magnetic field, showing that both flow and field induce orientational order in the dispersion. The anisotropy increases with the increase of field and with the increase of shear rate. Three states of order have been observed with the application of both shear flow and magnetic field. At low shear rates, the particles are aligned in the field direction. When increasing shear rate is applied, the particles revert to random orientations at a characteristic shear rate that depends on the strength of the applied magnetic field. Above the characteristic shear rate, the particles align along the flow direction. The experimental results agree qualitatively with the predictions of a mean field model.

Influence of pre-shearing on the crystallisation of conventional and metallocene polyethylenes

The influence of pre-shearing on the crystallisation of a conventional Ziegler–Natta catalysed and a metallocene catalysed linear low-density polyethylene (LLDPE) samples was studied by a rheo-optical method, coupling light scattering and steady shear flow. Experiments were performed on a high-temperature shearing cell, with a pair of parallel quartz plate windows. The polymers were sheared at a melt temperature T s (ranging from 190 to 150 °C) at a constant shear rate ( γ ̇ ) for a duration time t s. After cessation of shear (at a given deformation of γ ̇ t s unit), the sample was maintained at the selected melt temperature for a waiting time t w (ranging from 0 to 10 min) before it was cooled down to 90 °C. Small-angle light scattering (SALS) patterns were recorded during the whole process. It was shown that the pre-shear history thus investigated has no measurable influence on crystallisation of the linear metallocene LLDPE. For the Ziegler–Natta sample, the influence of pre-shear on its crystallisation is larger when the shear rate ( γ ̇ ) and strain ( γ ̇ t s ) are large, the waiting time t w is smaller or the temperature T s is lower. The consequence of shear is giving ellipsoidally deformed spherulites, elongated in the flow gradient direction, which originate from oriented nuclei. Crystallisation, following flow in particular, is shown to be a very good probe of chain orientation and it turns out to be more sensitive than classical linear rheological methods. It can detect if the sheared sample is in a steady state or if all chains have relaxed after a flow. For example, it is surprisingly shown that chain orientation for the Ziegler–Natta sample requires a large amount of shear deformation, in the order of 1000 strain units, to reach a steady state.

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions.