Newtonian Shear Flow Research Articles

An immersed boundary-lattice Boltzmann method for fluid-structure interaction problems involving viscoelastic fluids and complex geometries

An immersed boundary-lattice Boltzmann method (IB-LBM) for fluid-structure interaction (FSI) problems involving viscoelastic fluids and complex geometries is presented in this paper. In this method, the fluid dynamics and the constitutive equations of viscoelastic fluids are both solved using the lattice Boltzmann method. In order to enhance numerical stability in solving the constitutive equations, an artificial damping is introduced which does not affect the numerical results if the damping effect is much smaller than the relaxation and the convective effects. The structural dynamics including 2D and 3D capsules, 2D and 3D rigid particles and flags, are solved by the finite difference method (2D capsules, 2D and 3D rigid particles and flags) and the finite element method (3D capsules). The interaction between the solid structure and the fluid is enforced by an immersed boundary method. The overall framework of this method is very simple, enabling modelling FSI problems involving viscoelastic fluids and the inertia of both fluids and structures. It is very efficient for FSI problems involving high Weissenberg numbers flows, large deformations and complicated geometries without any preconditioner. This work uses IB-LBM to solve for the first time, flows involving viscoelastic fluids coupled with non-massless deforming structures. The method is also capable of solving very high Weissenberg number problems, as demonstrated by simulations of flexible particle flows at Wi=100. The present method and models are validated by several cases including a 2D rigid particle migration in a Giesekus Couette flow, a spherical particle rotation in an Oldroyd-B shear flow, a spherical particle settling in a FENE-CR fluid, 2D and 3D capsules deformation in a Newtonian shear flow, and a 3D flag flapping in a Newtonian free stream. In addition, the present method is also applied to simulate the deformation of 2D and 3D capsules in an Oldroyd-B shear flow, a 3D flag flapping in an Oldroyd-B free stream, and elastic capsule movement in a contraction-expansion channel filled with an Oldroyd-B fluid. Deformation of the capsules decreases with the increase of the Weissenberg number and the capsules experience monotonically increasing deformation when the Weissenberg number is above a critical value which is respectively 10 for 2D and 2 for 3D simulations. Viscoelasticity of the Oldroyd-B fluid hinders the flapping motion of the 3D flag. For elastic capsules passing through a periodic contraction-expansion channel, the capsules mix up after a short-term evolution, and then migrate to the bottom of the channel and almost follow two steady trajectories after a long-term evolution. The validations and applications provide extensive data which may be used to expand the currently limited database available for FSI benchmark studies.

Response of monoflagellate pullers to a shearing flow: A simulation study of microswimmer guidance

Microscale swimming may be intuited to be dominated by background flows, sweeping away any untethered bodies with the prevalent flow direction. However, it has been observed that many microswimmers utilize ambient flows as guidance cues, in some cases resulting in net motion upstream, contrary to the dominant background fluid direction and our accompanying intuition. Thus the hydrodynamic response of small-scale motile organisms requires careful analysis of the complex interaction between swimmer and environment. Here we investigate the effects of a Newtonian shear flow on monoflagellated swimmers with specified body symmetry, representing, for instance, the Leishmania mexicana promastigote, a parasitic hydrodynamic puller that inhabits the microenvironment of a sandfly vector midgut and is the cause of a major and neglected human tropical disease. We observe that a lack of symmetry-breaking cellular geometry results in the periodic tumbling of swimmers in the bulk, with the rotations exhibiting a linear response to changes in shearing rate enabling analytic approximation. In order to draw comparisons with the better-studied pushers, we additionally consider virtual Leishmania promastigotes in a confined but typical geometry, that of a no-slip planar solid boundary, and note that in general stable guided taxis is not exhibited amongst the range of observed behaviors. However, a repulsive boundary gives rise to significant continued taxis in the presence of shearing flow, a phenomenon that may be of particular pertinence to the infective lifecycle stage of such swimmers subject to the assumption of a Newtonian medium. We finally propose a viable and general in vitro method of controlling microswimmer boundary accumulation using temporally evolving background shear flows, based on the analysis of phase-averaged dynamics and verified in silico.

Dynamics of a flexible fibre in a sheared two-dimensional foam: Numerical simulations

Recently there has been a renewed interest in using foamy suspensions of wood fibres as a carrier fluid in papermaking but there is a lack of fundamental understanding of the dynamics of such a three-phase system. In this article we propose a numerical model for the dynamics of an individual flexible fibre within a flowing foam, based on discrete-element methods. As is observed in a Newtonian shear flow, we observe that the fibre systematically experiences a tumbling instability: the disordered motion of bubbles cannot prevent the pseudo-periodical flip of the fibre. Our simulations show that the tumbling time decreases almost as the inverse of the strain rate. It also decays when the fibre length is increased, asymptoting to a finite constant. The tumbling time is found to be independent of the stiffness of the fibre. Because of their tumbling motion, long and flexible fibres spend most of the time in a coiled geometry. This would imply that using foam as a carrier fluid is not enough to keep fibres aligned with the flow. However, further refinements of the model will need to be considered to arrive at firm conclusions regarding alignment.

Simulation of the Tape‐Laying Process for Thermoplastic Matrix Composites

AbstractThe paper presents an overview of the tape‐laying process for thermoplastic matrix composites and the current state‐of‐the‐art simulation of this process. As the current mathematical description of the process is partly based on a Newtonian shear flow and thermoplastics normally show a shear thinning behavior at higher shear rates, the assumption of a Newtonian shear flow has been verified. Therefore, the occurring shear rates have been calculated and compared with the data of a viscosity plot for a polyether ether ketone material. As a result of this analysis, the assumption of Newtonian shear flow is shown to be an oversimplification. © 2012 Wiley Periodicals, Inc. Adv Polym Techn 32: E705–E713, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/adv.21312

Vibration control of mechanical systems using semi-active MR-damper

The concept of structural vibration control is to absorb vibration energy of the structure by introducing auxiliary devices. Various types of structural vibration control theories and devices have been recently developed and introduced into mechanical systems. One of such devices is damper employing controllable fluids such as ElectroRheological (ER) or MagnetoRheological (MR) fluids. MagnetoRheological (MR) materials are suspensions of fine magnetizable ferromagnetic particles in a non-magnetic medium exhibiting controllable rheological behaviour in the presence of an applied magnetic field. This paper presents the modelling of an MR-fluid damper. The damper model is developed based on Newtonian shear flow and Bingham plastic shear flow models. The geometric parameters are varied to get the optimised damper characteristics. The numerical analysis is carried out to estimate the damping coefficient and damping force. The analytical results are compared with the experimental results. The results confirm that MR damper is one of the most promising new semi-active devices for structural vibration control.

Viscosity of curved fibers in suspension

In this paper, the relationship between fiber shape and relative viscosity of a fiber suspension is explored. A numerical simulation has been used to model non-Brownian curved rigid fibers in suspension under the influence of Newtonian shear flow. Curvature in the simulated fibers was taken to represent general deformities of real fibers in suspension. The simulation method was previously used by Joung et al. [J. Non-Newtonian Fluid Mech. 99 (2001) 1] to determine suspension viscosity for flexible fibers in suspension. When compared to the equivalent straight rigid fiber suspension, fiber curvature was found to contribute to a large increase in suspension viscosity. For typical semi-concentrated to concentrated suspensions, curved fibers were observed to produce viscosity increases of the order twice that of straight fiber suspensions. Results indicate that even a small bend in the fibers may cause a large bulk viscosity increase. Suspension viscosity is therefore highly dependent on the quality control measures taken during sample preparation.

Thermal convection over flat plates possessing an irregular leading edge

Boundary layer similarity reductions for thermal convection adjacent to inclined heated plates with an irregular leading edge are presented. The theory is outlined using three examples: Newtonian convection over an isothermal plate, Darcian convection over a nonuniformly heated plate, and mixed convection of Newtonian shear flow over a nonuniformly heated plate. These reductions represent a natural extension of results obtained by the author for Blasius flow over a flat plate with an irregular leading edge.

Relationships among shear stress jumps and high‐frequency dynamic viscosity of viscoelastic fluids

Linear viscoelastic fluid theory is used to demonstrate that the infinite frequency dynamic viscosity η’∞, the viscosity jump upon start‐up of shear flow η+(0), and the viscosity jump upon cessation of Newtonian shear flow η0−η−(0) are equal. Therefore, these quantities are fundamentally the same material property for fluids that exhibit linear viscoelastic behavior in the limit of small deformations. The η’∞ predictions of several continuum and molecular theories are compared, and implications for theoretical and experimental investigations of these phenomena are discussed.

Intrinsic viscosity of flexible polymers in unbounded and bounded Newtonian shear flow

The zero-shear-rate intrinsic viscosity of a polymer in an athermal and THETA solvent in free space and confined in a slit is investigated by Monte Carlo simulations of self-avoiding random walks on a simple cubic lattice. The intrinsic viscosity in a Newtonian shear flow is calculated by Zimm's algorithm. The results for an unbounded system are in excellent agreement with several scaling predictions. The intrinsic viscosity is below its unbounded value when the coil is squeezed. The effect of hydrodynamic interactions between walls and chain segments on the intrinsic viscosity is negligible. The differences between THETA and athermal solvent conditions gradually diminish with a decrease in the width of the slit as witnessed by the intrinsic viscosity and the scaling exponent for the radius of gyration. This is due to the fact that the solvent quality improves for a decreasing slit width; i.e., a THETA-solvent in three dimensions becomes a good solvent in two dimensions. The increase in excluded volume implies that there is a distinct difference between THETA-chains (i.e., chains that behave as random walks in free space) and real random walks. In the latter case the value of the component of the radius of gyration parallel to the walls is independent of the slit width. For real THETA-chains it increases.