On the use of genetic algorithm for finding the neutral instability curve in plane Poiseuille flow

A novel method based on genetic algorithm (GA) is proposed, to the best of our knowledge for the first time, for finding the neutral instability curve of the Orr-Sommerfeld equation in (nearly) parallel flows. New concepts such as “proximity of parents” and “gender discrimination” are added to the conventional GA in order for this algorithm to find the neutral instability curve. Certain GA operators such as “crossover” and “mutation” will also be modified in such a way that this algorithm can meet this purpose. To check the applicability of the modified genetic algorithm (MGA) developed in this work in finding the neutral instability curve, the case of plane Poiseuille flow will be used as a benchmark. It will be shown that the modified genetic algorithm developed in this work is well capable of determining the neutral instability curve for this particular flow geometry.     

Simulations of magnetorheological suspensions in Poiseuille flow

Particle-level simulations are conducted to study magnetorheological fluids in plane Poiseuille flow. The importance of the boundary conditions for the particles at the channel walls is examined by considering two extreme cases: no friction and infinite coefficient of friction. The inclusion of friction produces Bingham fluid behavior, as commonly observed experimentally for MR suspensions. Lamellar structures, similar to those reported for electrorheological fluids in shear flow, are observed in the post-yield region for both particle boundary conditions. The formation of these lamellae is accompanied by an increase in the bulk fluid velocity. The slip boundary condition produces higher fluid velocities and thicker lamellar structures.     

Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow

The thermal convection of a Jeffreys fluid subjected to a plane Poiseuille flow in a fluid-porous system composed of a fluid layer and a porous layer is studied in the paper. A linear stability analysis and a Chebyshev τ-QZ algorithm are employed to solve the thermal mixed convection. Unlike the case in a single layer, the neutral curves of the two-layer system may be bi-modal in the proper depth ratio of the two layers. We find that the longitudinal rolls(LRs) only depend on the depth ratio. Wi...     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

On the modeling of fluidity loss phenomena in Couette and Poiseuille flows of elastic liquids

Some effects of the possible relaxation transition from viscoelastic liquid state to highly elastic solid state were theoretically and numerically investigated in the shear situations, within the approach proposed in papers [1, 2, 5, 16]. It was found that for a single Maxwellian model the constitutive equations developed in [1, 2, 5] are not valid at elevated shear stresses. Some new aspects of the possible rheological behavior of elastic liquids in subcritical (before transition) and supercritical (after transition) regimes were demonstrated. The mechanism of fluidity loss studied in this paper could serve as a possible trigger mechanism for the melt flow instabilities.     

Dynamics of short fiber suspensions in bounded shear flow

We have studied the dynamics of non-colloidal short fiber suspensions in bounded shear flow using the Stokesian dynamics simulation. Such particles make up the microstructure of many suspensions for which the macroscopic dynamics are not well understood. The effect of wall on the fiber dynamics is the main focus of this work. For a single fiber undergoing simple shear flow between plane parallel walls the period of rotation was compared with the Jeffrey’s orbit. A fiber placed close to the wall shows significant deviation from Jeffrey’s orbit. The fiber moving near a solid wall in bounded shear flow follows a pole-vaulting motion, and its centroid location from the wall is also periodic. Simulations were also carried out to study the effect of fiber–fiber interactions on the viscosity of concentrated suspensions.     

Stability analysis in spatial mode for channel flow of fiber suspensions

Different from previous temporal evolution assumption, the spatially growing mode was employed to analyze the linear stability for the channel flow of fiber suspensions. The stability equation applicable to fiber suspensions was established and solutions for a wide range of Reynolds number and angular frequency were given numerically . The results show that, the flow instability is governed by a parameter H which represents a ratio between the axial stretching resistance of fiber and the inertial force of the fluid. An increase of H leads to a raise of the critical Reynolds number, a decrease of corresponding wave number, a slowdown of the decreasing of phase velocity , a growth of the spatial attenuation rate and a diminishment of the peak value of disturbance velocity. Although the unstable region is reduced on the whole, long wave disturbances are susceptible to fibers.     

On the accuracy of the calculation of transient growth in plane Poiseuille flow

This paper addresses the accuracy of numerical methods to compute the transient energy growth of plane Poiseuille flow. We show that using the Chebyshev collocation method to discretize the linearized governing equations in the wall‐normal direction can introduce numerical problems when computing the energy evolution of the flow. We demonstrate that spurious eigenmodes of the discretized linear operator and numerical integration errors are the possible sources of the numerical problems, and we also show that spurious eigenvalues with negative real parts of large magnitude can affect the calculation of energy growth. These difficulties can be avoided by using a spectral Galerkin method where the basis functions satisfy the boundary conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Constitutive equations for fiber suspensions in viscoelastic media

The kinetic theory of elastic dumbells with a friction factor that depends on the fiber orientation is used to obtain constitutive equations for fiber suspensions in a polymer matrix. We followed the approach of Fan (X.J. Fan, in P. Moldenaers and R. Keunings (Eds.), Theoretical and Applied Rheology, Proceedings XIth International Congress on Rheology, Brussels, Elsevier, Amsterdam, 1992, pp. 850–852), and derived equations for polymer solutions based on the FENE-P, FENE-CR, and Giesekus models. Start-up and steady-state free shear flows are studied to explore the effects of the fiber-polymer coupling as well as the fiber volume fraction. Predictions based on different types of closure approximations for the fourth-order fiber orientation tensor are also discussed.     

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.The project supported by the National Natural Science Foundation of China (10372090) and Doctoral Program of Higher Education in China (20030335001)The English text was polished by Ron Marshall     

Convective and absolute instabilities in counter-rotating spiral Poiseuille flow

We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent numerical investigations done by Pinter et al. [24] by measuring the absolute and convective stability boundaries of both propagating Taylor vortices (PTV) and spiral vortices (SPI). Thus our work shows that these theoretical concepts from hydrodynamic stability in open flows apply to experimental counter-rotating Taylor–Couette systems with an imposed axial through flow. PACS 47.20.-k, 05.45.-a, 47.15.fe     

Rheo-optics of hydroxypropylcellulose solutions in Poiseuille flow

The behavior of an aqueous solution of hydroxypropylcellulose in the liquid crystalline phase is investigated when it is flowing in a rectangular channel. Rheological characterization shows that the viscosity vs. shear rate curve follows the typical three region pattern, with the intermediate plateau of region II extending over a relative large range of shear rates (more than one decade). Two complementary rheo-optical determinations are performed. Velocity profiles across the channel thickness are measured by a hydrogen bubble visualization technique. Texture evolution is monitored by in situ optical microscopy. Accurate focusing inside the sample thickness allows observation in real time of the texture at various shear rates, as generated in the Poiseuille type of flow in the channel. It is shown that the velocity profiles can be accurately predicted by assuming that the flow in the channel is purely viscous, and using only the viscosity data described above. It is also shown that the morphology of the texture generated inside the flowing system is a function of the local shear rate. In particular, an elongated structure is observed when the shear rate exceeds the critical value corresponding to the onset of region II in the viscosity curve.     

Instability of a horizontal plane-channel flow of a dilute suspension

The stability of a horizontal plane-channel flow of a dilute suspension is studied theoretically. It is shown that the mechanism of action of the sedimenting particles on the flow stability parameters is equivalent to the effect of a distributed flow stratification and is attributable to the vertical nonuniformity of the body force induced by the excess weight of the sedimenting particles. A strong dependence of the disturbance growth rate on the location of the interface between the suspension and the pure liquid is detected.     

Effect of random longitudinal vibrations on the Poiseuille flow of a complex liquid

In this work, the rectilinear Poiseuille flow of a complex liquid flowing in a vibrating pipe is analyzed. The pipe wall performs oscillations of small amplitude that can be adequately represented by a weakly stochastic process, for which a quasi-static perturbation solution scheme is suggested. The flow is analyzed using the Bautista–Manero–Puig constitutive equation, consisting on the upper-convected Maxwell equation coupled to a kinetic equation to account for the breakdown and reformation of the fluid structure. A drastic enhancement of the volumetric flow is predicted in the region where the fluid experiences pronounced shear-thinning. Finally, flow enhancement is predicted using experimental data reported elsewhere for wormlike micellar solutions of cetyl trimethyl ammonium tosilate.     

The linear stability of plane Poiseuille flow under unsteady distortion

This paper investigates the linear stability behaviour of plane Poiseuille flow underunsteady distortion by multiscale perturbation method and discusses further the problemproposed by paper[1].The results show that in the initial period of disturbancedevelopment,the distortion profiles presented by paper[1]will make the disturbances growup,thus augmenting the possibility of instability.     

Investigation of fiber motion near solid boundaries in simple shear flow

In this paper, fiber motion near a planar wall was investigated using a planar shear flow apparatus. Fibers were placed (one at a time) perpendicular to the flow direction at various locations throughout the flow field. The location and orientation of each fiber versus time was measured, using an image processing system, until the fiber aligned with the flow direction. When the centroid of the fiber was located at distances greater than a fiber length from the wall, Jeffery's equations governing particle motion were verified. For distances less than a fiber length and greater than a fiber diameter from the wall, the fiber experienced an increased rate of rotation. In this regime, the motion of the fiber could be described by Jeffery's equations if an increased effective shear rate was used. The effective shear rate was found to increase logarithmically with decreasing separation distance. The wall effect was higher for longer aspect ratio fibers and was also a function of orientation; fibers oriented perpendicular to the wall rotated faster than those oriented parallel to the wall at the same separation distance. Once the fiber aligned with the flow direction, it ceased to rotate within the field of view. In this orientation, the wall had a stabilizing effect on the fiber. In efforts to relate the increase in shear rate to the aspect ratio of the fiber and the separation distance between the fiber and a solid wall, a translation model based on the work of De Mestre and Russel was explored. This model allows one to quantify the increase in shear rate experienced by the fiber due to the presence of a wall or obstruction in the flow field. However, the model has its limitations and care should be taken when applying this model outside its realm of validity. When compared to experimental data, the translation model provides a very good estimate of the increased shear rate experienced by the fiber when it is located less than 2/3 of a fiber length from a planar wall. Received: 20 April 2000 Accepted: 28 September 2000     

Shear-thickening flow of suspensions of carbon nanofibers in aqueous PVA solutions

The suspensions of carbon nanofibers in aqueous poly(vinyl alcohol) solutions were prepared in the presence of spherical carbon black particles, and the steady-shear viscosity and dynamic viscoelasticity were measured for complex suspensions. Although the single suspensions of carbon black are highly stable, the flocculation of carbon nanofibers is promoted by the addition of carbon black particles. The complex suspensions show remarkable shear thickening in the steady-flow and strain hardening in oscillatory shear with large amplitude. The nonlinear responses strongly depend on the carbon black concentration, whereas the dynamic viscoelasticity at low strains in the linear ranges is not significantly influenced. As the highly elastic effects arise from the long-range motion of particles, the possible mechanism may be the orientation of nanofibers in strong shear fields. The suspensions show the time-dependent behavior of viscosity when the time-scale of measurements is shorter than that of structural recovery to the isotropic states.     

Stokes eigenfunctions and Galerkin projection of the disturbance equations in plane Poiseuille flow: a systematic analytical approach

In the present paper, the L ²-normalized Stokes eigenfunctions for plane Poiseuille flow, which form an orthonormal functional basis for the space of disturbances, are written in a general exponential form. Then, the evolution equations for the disturbances are Galerkin-projected on the considered basis functions, and all the terms of the resulting dynamical system are expressed systematically in analytical form. Finally, a numerical example is given in which the proposed basis functions are used for the simulation of the time evolution of the critical disturbance predicted by the energetic stability theory.     

Orientation distribution of fibers and rheological property in fiber suspensions flowing in a turbulent boundary layer

A model relating the translational and rotational transport of orientation distribution function （ODF） of fibers to the gradient of mean ODF and the dispersion coefficients is proposed to derive the mean equation for the ODE Then the ODF of fibers is predicted by numerically solving the mean equation for the ODF together with the equations of turbulent boundary layer flow. Finally the shear stress and first normal stress difference of fiber suspensions are obtained. The results, some of which agree with the available relevant experimental data, show that the most fibers tend to orient to the flow direction. The fiber aspect ratio and Reynolds number have significant and negligible effects on the orientation dis- tribution of fibers, respectively. The additional normal stress due to the presence of fibers is anisotropic. The shear stress of fiber suspension is larger than that of Newtonian solvent, and the first normal stress difference is much less than the shear stress. Both the additional shear stress and the first normal stress difference increase with increasing the fiber concentration and decreasing fiber aspect ratio.