A coordinate frame for helical flows

This note presents a coordinate frame representation for the conservation laws governing fluid motion in a helical configuration as suggested by a single-screw extruder with deep flights and by the Kenics Static Mixer. This example demonstrates the care necessary in dealing with nonorthogonal coordinate systems. The conservation equations are also presented in terms of the proper physical components, as well as the physical components of the rate of deformation tensor. The paper closes with a brief statement of the boundary conditions for flow in a static mixer.     

Entry and exit flows of casson fluids

Entry and exit flows through abrupt contractions are studied numerically for Casson fluids exhibiting a yield stress. The Casson constitutive equation recommended for describing blood flow is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of unyielded/yielded regions along with the swelling ratio of the free stream for planar and axisymmetric contraction flows for the whole range of Casson numbers. The results for pressure are used to determine the excess pressure losses that give rise to entrance, exit, and the total end correction.     

Electrorheological fluids based on polymer electrolytes

The phenomenon of electrorheological activity taking part in so called electrorheological fluids (ERFs) relies on strong and reversible changes of fluid viscosity upon application of electric field and finds interesting technical applications. ERFs typically comprise dispersions of polarisable solid particles in liquid matrices. The paper describes studies on complexes of polyacrylonitrile with various salts of alkaline elements. The materials in a powder form were dispersed in silicone oil as well as in active matrices containing a liquid crystalline polymer. It was found that these novel systems were substantially anhydrous and electrorheologically active. The observed ER effect was relatively high and accompanied by very low current consumption. The magnitude of the ER effect was correlated with bulk ionic conductivity of the studied materials. The optimal bulk conductivity giving the highest ER effect at reasonably low currents amounted to about 10⁻⁵ S/cm. Higher conductivities resulted in higher currents only and saturation of the yield stress values. It was also shown that dispersions of the polymer complexes in a solution of poly(n-hexyl isocyanatye) in xylene manifested enhanced ER activity.     

Laminar dispersion of polymer solutions in helical coils

In the present study the step response experiments were carried out with power law fluids in two helical coils to examine the suitability of axial dispersed plug flow model in describing the laminar dispersion of non-Newtonian fluids in helical coils. The ranges of variables covered are 10 ≤ λ ≤ 100,0.01 ≤ N_Regen ≤ 2.5,0.001 ≤ N_De ≤ 0.77 and 0.035 ≤ τ ≤ 1.33. It is found that coiling results in reduced dispersion to that in a straight tube.     

Crosswise ridge micromixers with split and recombination helical flows

This study presents a novel crosswise ridge micromixer (CRM) with a series of microstructures placed on the top and bottom floors of channels. Passive micromixers fabricated by Micro Electro-Mechanical Systems (MEMS) technologies with slanted ridges are investigated. Numerical simulations and experimental investigations are undertaken to determine the effects of various microstructure patterns on mixing efficiency with Reynolds numbers (Re) of 0.05–50. The confocal images at the cross-sections along the channel with ridges on both the channel top and bottom are first investigated in our study. A significant amount of split and recombination (SAR) helical flows is produced by the slanted ridges embedded on the two floors of the channels. The effects of non-dimensional parameters, such as the Re, as well as geometrical parameters on mixing performance are presented in terms of the mixing index. When the Re exceeds 1, the mixing index of the micromixer with slanted ridges increases as the Re increases further. Simulation results are presented and compared with experimental data. The trends of the experimental results and numerical data are very similar. Finally, various numbers of slanted ridges in the same orientation in one channel cycle are investigated to determine mixing performance in microchannels. The mixing performance achieves an optimum value in case where the number of ridges per cycle is equal to 8.     

Structure formation during polymer blend flows

The structure formation processes that occur during the flow of dilute blends of high density polyethylene (HDPE) or polypropylene (PP) In a linear low density polyethylene (LLDPE) carrier phase have been studied. Due to low surface tensions, high deformations of the dispersed minor phase can be induced under slow flow conditions leading to the formation of slender filaments. Measurements on a slit die, having a large, converging flow entrance region, demonstrate that the mechanism for filament formation is droplet bursting, yielding growing tails during shear flow, or, unsteady drop elongation during extensional flow. Tail growth can be modeled as the flow of a slightly tapering cylinder in a fluid of different viscosity, For dispersed to carrier phase viscosity ratios greater than unity, extensional flow occurs in the tail phase, which can induce oriented crystallization. For ratios less than unity, the flow is compressive, which. Inhibits crystallization. Drop deformation and crystallization in the converging flow entrance region is greatly enhanced by the extensional flow, and droplet growth can be described by a model assuming a time-dependent, planar, extensional flow field. Data for birefringence and melting points of as-crystallized fibers are also presented and discussed.     

Entrance laminar flows of viscoplastic fluids in concentric annuli

Developing flows of generalized Bingham (Herschel-Bulkley) fluids in concentric annuli were studied numerically. A control volume approach based upon an upwinding finite difference technique was used to solve the equation of motion. The results in terms of velocity and pressure drop profiles are shown graphically. Radius ratios of 0.02, 0.2, 0.4 and 0.6; power-law indices (n) of 0.7, 1.0 and 1.2; generalized Bingham numbers of 5, 10 and 15 were investigated. At present, there are no experimental results with which to make comparisons. However, there are results for fully developed flows and comparison has been made with these. In all cases the agreement was good.     

Process viscometry of complex fluids and suspensions with helical ribbon agitators

The viscosity of highly inelastic shear thinning fluids and aqueous suspensions of kaolin clay particles has been investigated using a helical ribbon impeller fitted to a rheometer. Viscosity data for the single phase non-Newtonian fluids adequately processed with a generalized Reynolds number based on the impeller tip speed are shown to superimpose very well to the results obtained with a cone and plate rheometer. In the case of the two-phase system, it is shown that the data treatment for single phase system can be extended. The helical ribbon impeller yields more stable viscosity values than with the traditional geometries and no spurious flow phenomena (i.e., sedimentation, slip at the wall, etc.) was observed, making this system a superior device for suspension rheology over cone and plate and Couette flow rheometers.     

Rayleigh-Jeffreys stability of thermohaline stratified fluids subject to vertical flows

The stability of an infinite horizontal layer of fluid with a density stratification due to both temperature and solute gradients, subject to an initial vertical flow field, is studied for different sets of homogeneous boundary conditions. Sufficient conditions for the maintenance of the original stratification, i.e., for stability, are obtained as a relation between R_aT, the thermal Rayleigh number, and R_as, the solute Rayleigh number. The relation $\text{R}{}_{\mathrm{as}}\text{R}{}_{\mathrm{aT}}$<-($\text{P}{}_{\mathrm{s}}\text{P}{}_{\mathrm{T}}$) is obtained as a sufficient condition for stability for all sets of boundary conditions, where P_T and P_S are the thermal and solute Prandtl number, respectively. This condition may thus be applied to cases in which the physical boundary conditions are not well defined; e.g., to practical engineering use of solar ponds.In addition, in conjunction with a similar result for initial horizontal flow fields, the result gives a sufficient condition for stability of arbitrary initial flows under all combinations of boundary conditions.     

Elongational,hysteresis, and oscillatory flows of complex fluids

The simple model proposed earlier to describe te rheological properties of complex fluids is used to calculate (a) the extensional viscosity, (b) the hysteresis loops, and (c) the complex viscosity. It has been found that the rheological properties predicted by the model agree with experimental observations. It is shown that for some viscoelastic fluids the extensional viscosity is always finite and for some other fluids the extensional viscosity tends t infinity at finite extensional rate. In the latter case, steady flow is not attainable. The shape of the hysteresis loops depends on the maximum shear-rate. It also depends on the material properties. In a small amplitude oscillatory flow, our model reduces t a linear viscoelastic fluid.     

Implications of extensional flows in polymer fabrication processes

The various types of extensional flows and extensional viscosities are defined and methods of measurement discussed. The role that each of these extensional viscosities plays in various polymer fabrication processes is discussed with examples. Finally, it is shown how engineering analyses of these complex flow fields are conducted using simplified phenomenological equations for the rheological behavior. This approach is recommended for use until such time as tensorially correct, mathematically tractable constitutive equations that are based on molecular theory are available.     

Rayleigh-Jeffreys stability of thermohaline stratified fluids subject to horizontal flows

The stability of a horizontal layer of a fluid with density stratification due to both temperature and solute gradients, subject to horizontal flow, is studied for different sets of homogeneous boundary conditions. Sufficient conditions for stability, i.e., the maintenance of the original stratification are obtained as the relation between the thermal Rayleigh number, R_aT, and the solute Rayleigh number, R_aS. For stabilizing solute gradients —<-R_aS/R_aT<(P_rS/P_rT)² is obtained as a sufficient condition for stability for all sets of boundary conditions, where P_rT and P_rS are the thermal and the solute Prandtl numbers, respectively. This condition is, therefore, also applicable in cases where the physical boundary conditions are not well defined, e.g., in practical engineering use of solar ponds.     

Immiscible polymer blend electrorheological fluids: Composition dependence

We investigated the composition dependence of the electrorheological properties of immiscible polymer blends which consist of liquid crystalline polymers (LCPs) and polydimethylsiloxane (DMS). We used two different kinds of LCPs, designated as A and B polymers. We observed that for a fixed ratio of an LCP and DMS (LCP:DMS = 2:1) the electrorheological properties change from type I to type II as the fraction of the A polymer is reduced. Microscopic observations indicate that the change in the electrorheological properties is associated with the structural change; in type I, LCP droplets are dispersed in DMS, while in type II, DMS droplets are dispersed and, furthermore, that the structural change is associated with the miscibility between DMS and the LCPs; the A polymer is partially miscible with DMS, while the B polymer is hardly miscible with DMS. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 3673–3680, 2002     

Power consumption of helical ribbon mixers in viscous newtonian and non-newtonian fluids

Power input measurements are reported for helical ribbon impellers for two scales; a 0.15 m diameter and a 0.4 m diameter tank. Data for viscous Newtonian and non-Newtonian fluids are brought together by use of the average apparent viscosity concept and the following equation:

where k_s is the shear rate constant, c is the clearance between vessel wall and impeller with diameter D.Power measurements from this work combined with relevant information extracted from the published literature indicate that impeller geometry has a profound effect upon power requirement, particularly in the laminar region, where the reported data can be described by:

where K_p is a geometric constant and all the other symbols have their usual significance. Theoretical models which fail to allow for system geometry and fluid properties give values which may be seriously in error.     

The descent into glass formation in polymer fluids

Glassy materials have been fundamental to technology since the dawn of civilization and remain so to this day: novel glassy systems are currently being developed for applications in energy storage, electronics, food, drugs, and more. Glass-forming fluids exhibit a universal set of transitions beginning at temperatures often in excess of twice the glass transition temperature T(g) and extending down to T(g), below which relaxation becomes so slow that systems no longer equilibrate on experimental time scales. Despite the technological importance of glasses, no prior theory explains this universal behavior nor describes the huge variations in the properties of glass-forming fluids that result from differences in molecular structure. Not surprisingly, the glass transition is currently regarded by many as the deepest unsolved problem in solid state theory. In this Account, we describe our recently developed theory of glass formation in polymer fluids. Our theory explains the origin of four universal characteristic temperatures of glass formation and their dependence on monomer-monomer van der Waals energies, conformational energies, and pressure and, perhaps most importantly, on molecular details, such as monomer structure, molecular weight, size of side groups, and so forth. The theory also provides a molecular explanation for fragility, a parameter that quantifies the rate of change with temperature of the viscosity and other dynamic mechanical properties at T(g). The fragility reflects the fluid's thermal sensitivity and determines the manner in which glass-formers can be processed, such as by extrusion, casting, or inkjet spotting. Specifically, the theory describes the change in thermodynamic properties and fragility of polymer glasses with variations in the monomer structure, the rigidity of the backbone and side groups, the cohesive energy, and so forth. The dependence of the structural relaxation time at lower temperatures emerges from the theory as the Vogel-Fulcher equation, whereas pressure and concentration analogs of the Vogel-Fulcher expression follow naturally from the theory with no additional assumptions. The computed dependence of T(g) and fragility on the length of the side group in poly(α-olefins) agrees quite well with observed trends, demonstrating that the theory can be utilized, for instance, to guide the tailoring of T(g) and the fragility of glass-forming polymer fluids in the fabrication of new materials. Our calculations also elucidate the molecular characteristics of small-molecule diluents that promote antiplasticization, a lowering of T(g) and a toughening of the material.     

Mathematical modeling of squashing flows of heated polymer particles

A combination of shear and extension is encountered in the squashing flows of heated polymer particles. Extensional rate affects the non-Newtonian viscosity in determining the flow field in the squashing of cylindrical particles, but both the extensional and shear rates are equally important for disc-like particles. A viscous-type constitutive equation is used for simplicity. The solution of the momentum equations satisfying no-slip boundary conditions leads to a particle flattening equation that can predict flattening ratios of nonisothermal particles in terms of rheological parameters and dimensionless groups of process variables. Application of this analysis to roll fusing of toner particles in copiers is described in a companion article in this issue.     

Propulsion efficiency of achiral microswimmers in viscoelastic polymer fluids

We report the effects of polymer size, concentration, and polymer fluid viscoelasticity on the propulsion kinematics of achiral microswimmers. Magnetically driven swimmer's step-out frequency, orientation angle, and propulsion efficiency are shown to be dependent on fluid microstructure, viscosity, and viscoelasticity. Additionally, by exploring the swimming dynamics of two geometrically distinct achiral structures, we observe differences in propulsion efficiencies of swimmers. Results indicate that larger four-bead swimmers are more efficiently propelled in fluids with significant elasticity in contrast to smaller 3-bead swimmers, which are able to use shear thinning behavior for efficient propulsion. Insights gained from these investigations will assist the development of future microswimmer designs and control strategies targeting applications in complex fluids.     

Mechanical degradation of semi-dilute polymer solutions in laminar flows

Mechanical degradation of a semi-dilute solution of non-hydrolyzed polyacrylamide was studied under laminar flow conditions through fine capillary systems. Using a multi-pass device and capillary tubes of the same diameter and of various lengths we have shown that mechanical degradation (i) occurs at a critical value of the wall shear rate, chosen as a reference deformation rate, which is slightly higher than that of the appearance of high pressure losses in the entrance region of the capillary tube; (ii) is independent of the capillary tube length; (iii) increases with the number of passes N up to a maximum value for a limiting number of passes N_lim which is a decreasing function of deformation rates but does not depend on capillary length. The amount of degradation is expressed in terms of loss of viscous dissipation in shear and transient elongational flow. This last point is determined by studying the total end pressure loss through the capillary tube as a function of the pass number. The high pressure loss is related to viscous dissipation on macromolecules stretched by rapid converging flow. A comparison between a fresh and a fully degraded solution indicates that the degradation affects shear viscosity much less than viscous dissipation in rapid converging flow which is related to the properties of extended macromolecules. Both experimental results and theoretical interpretation suggest that, in our capillary system, the mechanical degradation occurs in the entrance region of the capillary where macromolecules are stretched and consequently submitted to extensional forces which can overcome the C–C bonds strength.