Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOnset of transient shear banding in viscoelastic shear start-up flows: Implications from linearized dynamics
158
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We analyze transient dynamics during shear start-up in viscoelastic flows between two parallel plates, with a specific focus on the signatures for the onset of transient shear banding using the Johnson-Segalman, non-stretching Rolie-Poly and Giesekus models. We explore the dynamics of shear start-up in monotonic regions of the constitutive curves using two different methodologies: (i) the oft-used `frozen-time linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed on instantaneous stress components (treated as quasi steady states) exhibit exponential growth, and (ii) the more mathematically rigorous fundamental-matrix approach that characterizes the transient growth via a numerical solution of the time-dependent linearized governing equations, wherein the linearized perturbations co-evolve with the start-up shear flow. Our results reinforce the hitherto understated point that there is no universal connection between the overshoot and subsequent decay of shear stress in the base state and the unstable eigenvalues obtained from the frozen-time stability analysis. It may therefore be difficult to subsume the occurrence of transient shear banding during shear start-up within the ambit of a single model-independent criterion. Our work also suggests that the strong transients during shear start-up seen in earlier work could well be a consequence of consideration of the limit of small solvent viscosity in the absence of otherwise negligible terms such as fluid inertia.
rate research
Read More
Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume fraction, alternated in the vorticity direction and aligned with the flow (shear bands). These bands are associated with a decrease of the effective viscosity of the system. To understand the mechanism of banding experimentally observed we have performed interface resolved simulations of the two-fluid system. The experiments were perfomed starting with a random distribution of droplets which, under the applied shear, evolves in time resulting in a phase separation. To numerically reproduce this process, the banded structures are initialized in a narrow channel confined by two walls moving in opposite direction. We find that the initial banded distribution is stable when droplets are free to merge and unstable when coalescence is prevented. In this case, additionally, the effective viscosity of the system increases, resembling the rheological behavior of suspensions of deformable particles. Droplets coalescence, on the other hand, allows emulsions to reduce the total surface of the system and hence the energy dissipation associated to the deformation, which in turn reduces the effective viscosity.
To understand the behavior of composite fluid particles such as nucleated cells and double-emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimenstion-two point. We adopt a dynamical system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.
We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.
We present a modification of a recently developed volume of fluid method for multiphase problems, so that it can be used in conjunction with a fractional step-method and fast Poisson solver, and validate it with standard benchmark problems. We then consider emulsions of two-fluid systems and study their rheology in a plane Couette flow in the limit of vanishing inertia. We examine the dependency of the effective viscosity on the volume-fraction (from 10% to 30%) and the Capillary number (from 0.1 to 0.4) for the case of density and viscosity ratio 1. We show that the effective viscosity decreases with the deformation and the applied shear (shear-thinning) while exhibits a non-monotonic behavior with respect to the volume fraction. We report the appearance of a maximum in the effective viscosity curve and compare the results with those of suspensions of rigid and deformable particles and capsules. We show that the flow in the solvent is mostly a shear flow, while it is mostly rotational in the suspended phase; moreover this behavior tends to reverse as the volume fraction increases. Finally, we evaluate the contributions to the total shear stress of the viscous stresses in the two fluids and of the interfacial force between them.
Motivated by problems arising in the pneumatic actuation of controllers for micro-electromechanical systems (MEMS), labs-on-a-chip or biomimetic soft robots, and the study of microrheology of both gases and soft solids, we analyze the transient fluid--structure interaction (FSIs) between a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin--Voigt-type linearly viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tubes radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact (but implicit) solutions for the pressure for steady flow conditions. Second, we solve the transient problem of impulsive pressurization of the tubes inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to FSI coupling. The hydrodynamic pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube deformation is similar to that of a band-pass filter.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
