Measurements of mass transfer between particles and gas in packed tubes at very low tube to particle diameter ratios

Experimental results for the mass transfer between spherical naphthalene particles and air in packed tubes of very low tube to particle diameter ratio (D/d=1.41, 1.98, and 3.77) are presented. During the experiments the Reynolds number (2.4Re ₀<1500), the=" bed=" length,=" and=" the=" test=" temperature=" have=" been=" varied.=" data=" reduction=" has=" been=" carried=" out=" with=" and=" without=" accounting=" for=" axial=" dispersion=" in=" the=" model.=" the=" measured=" sherwood=" numbers=" are=" compared=" with=" the=" predictions=" according=" to=" the=" correlation=" of=" gnielinski=" and=" of=" wakao/funazkri,=" originally=" developed=" for=" large=" packed=" beds.=" the=" porosity=" of=" packings=" at=">D/d-ratios is discussed.Es werden Versuchsergebnisse über die Stoffübertragung zwischen kugelförmigen Naphthalinpartikeln und Luft in Festbetten mit sehr kleinem Verhältnis zwischen dem Rohr- und dem Partikeldurchmesser (D/d=1,41, 1,98 und 3,77) mitgeteilt. Während der Experimente wurden die Reynoldszahl (2,4Re ₀<1500), die=" bettlänge=" und=" die=" temperatur=" variiert.=" die=" versuchsauswertung=" erfolgte=" sowohl=" mit=" als=" auch=" ohne=" berücksichtigung=" der=" axialen=" dispersion.=" die=" experimentell=" ermittelten=" sherwoodzahlen=" werden=" mit=" den=" voraussagen=" der=" korrelationen=" von=" gnielinski=" und=" von=" wakao/funazkri=" verglichen;=" beide=" korrelationen=" wurden=" für=" betten=" mit=" einem=">D/d-Verhältnis entwickelt. Außerdem wird die Porosität von Betten im Bereich kleinerD/d-Quotienten behandelt.Dedicated to Prof. Dr.-Ing. K. Stephan on the occasion of his 60th birthday     

The mirror relations and nonlinear viscoelasticity of polymer melts

An attempt is made to incorporate into a quasilinear viscoelastic constitutive equation of the Boltzmann superposition type the two mirror relations of Gleissle, as well as his relation between the steady-state first normal-stress difference and the shear viscosity curve. It is shown that the three relations can hold separately within this constitutive model, but not simultaneously, because they require a different nonlinear strain measure, namelyS ₁₂ () = – a ( – 1) (a = 0 for 1,a = 1 for 1) for the mirroring of the viscosities,S ₁₂ () = – a (–k ²/) (a = 0 for k, a = 1 for k) for the mirroring of the first normal-stress coefficients, and for the third relation. Here denotes the shear strain and erf the error function. Experimental data on melts of a low-density polyethylene, a high-density polyethylene and a polypropylene show that the mirror relations are passable approximations, but that the third relation meets reality surprisingly close if the right value ofk is used.     

Scattering of elastic waves from symmetric inhomogeneities at low frequencies

The problem of the scattering of elastic waves is treated in the low-frequency regime by a systematic expansion in powers of the frequency in the spatial domain of the scatterer. The zeroth and first degree scattering amplitudes vanish if the scatterer is localized in all directions. The second degree scattering amplitude corresponds to the so called Rayleigh regime in which the quasi-static result of Gubernatis et al. is valid. In general, the third and higher degree scattering amplitudes are nonvanishing. However, in the case where the scatterer has inversion symmetry about the origin, it is shown that the third degree scattering amplitude vanishes identically for all incident and scattered directions and for all polarizations. This result implies that the frequency derivative of the phase shift approaches zero at least quadratically as the frequency goes to zero. In other words, at sufficiently low frequencies the effective scattering center of a scatterer with inversion symmetry is its geometrical center. The use of this result in the processing of experimental scattering data is discussed.     

The influence of matrix viscoelasticity on the rheology of polymer blends

We examine the effects of matrix phase viscoelasticity on the rheological modeling of polymer blends with a droplet morphology. Two contravariant, second-rank tensor variables are adopted along with the translational momentum density of the fluid to account for viscoelasticity of the matrix phase and the ellipsoidal droplet shapes. The first microstructural variable is a conformation tensor describing the average extension and orientation of the molecules in the matrix phase. The other microstructural variable is a configuration tensor to account for the average shape and orientation of constant-volume droplets. A Hamiltonian framework of non-equilibrium thermodynamics is then adopted to derive a set of continuum equations for the system variables. This set of equations accounts for local conformational changes of the matrix molecules due to droplet deformation and vice versa. The model is intended for dilute blends of both oblate and prolate droplets, and droplet breakup and coalescence are not taken into account. Only the matrix phase is considered as viscoelastic; i.e., the droplets are assumed to be Newtonian. The model equations are solved for various types of homogeneous deformations, and microstructure/rheology relationships are discussed for transient and steady-state conditions. A comparison with other constrained-volume rheological models and experimental data is made as well.     

A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites

The dynamics of polymer melts and concentrated solutions reinforced with nanoscale rigid spherical particles is analyzed. Nanocomposites with low filler volume fraction and strong polymer-filler interactions are considered. Entanglement effects are represented by requiring the diffusion in the chain contour direction to be more pronounced than in the direction transverse to the chain primitive path. Filler particles are treated as material points. They reduce the polymer mobility in both longitudinal and transverse tube directions due to short-range energetic filler-polymer interactions. Hence, the contribution to chain dynamics and stress production of both filler-polymer and polymer-polymer interactions is considered to be purely frictional in nature. In the model, the strain rate sensitivity is associated with the thermal motion of chains, with the convective relaxation of entanglement constrains and with the polymer-filler attachment/detachment process. The effect of model parameters is discussed and the predictions are compared with experimental data.     

Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions

The current state of understanding for solution conformations of flexible polymers and their linear viscoelastic response is reviewed. Correlation length, tube diameter, and chain size of neutral polymers in good solvent, neutral polymers in θ-solvent, and polyelectrolyte solutions with no added salt are compared as these are the three universality classes for flexible polymers in solution. The 1956 Zimm model is used to describe the linear viscoelasticity of dilute solutions and of semidilute solutions inside their correlation volumes. The 1953 Rouse model is used for linear viscoelasticity of semidilute unentangled solutions and for entangled solutions on the scale of the entanglement strand. The 1971 de Gennes reptation model is used to describe linear viscoelastic response of entangled solutions. In each type of solution, the terminal dynamics, reflected in the terminal modulus, chain relaxation time, specific viscosity, and diffusion coefficient are reviewed with experiment and theory compared. Overall, the agreement between theory and experiment is remarkable, with a few unsettled issues remaining.     

A study of viscoelasticity and extrudate distortions of wood polymer composites

Natural fiber composites exhibit a characteristic surface tearing and extrudate distortions upon exiting from extrusion dies. This type of defect is characterized by highly rough, cracked, and distorted extrudate surface. In this study, the extrudate distortions and viscoelastic nature of metallocene-catalyzed polyethylene (mPE)/wood flour composites have been investigated. As the wood flour loading increases the region of linear viscoelasticity shortens. The first normal stress difference decreases, while the storage modulus increases. It was observed that increasing the wood flour loading up to 50 wt% aggravated the surface tearing; however, 60 wt% wood flour in mPE completely eliminated the surface defect. It was also found that increasing the shear rate improved the surface appearance of the filled compounds. This is due to the increased wall slip velocity of the composites at high shear rates and wood filler loadings. Increasing the diameter of the die at the same aspect ratio generally provides more severe surface tearing. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Measurements of turbulent flow in a channel at low Reynolds numbers

Normal and streamwise components of the velocity fields of turbulent flow in a channel at low Reynolds numbers have been measured with laser-Doppler techniques. The experiments duplicate the conditions used in current direct numerical simulations of channel flow, and good, but not exact, agreement is found for single-point moments through fourth order. In order to eliminate LDV velocity bias and to measure velocity spectra, the mean time interval between LDV signals was adjusted to be much smaller than the smallest turbulence time scale. Spectra of the streamwise and normal components of velocity at locations spanning the channel are presented.     

Modelling of ER squeeze films at low amplitude oscillations

An experimental investigation of electrorheological squeeze film dynamics is presented for constant applied voltage and low strain amplitude. Both broadband random and sinusoidal motion are examined to explain complex film dynamics. Spectral results indicate a primarily elastic response with slip at the plate boundaries. By examining the evolution of an effective shear modulus over time, sinusoidal results show that slip at the boundaries is due to a solvent layer which may be modelled as a separate variable thickness squeeze film.     

Effects of the polydispersity on the viscoelasticity of low molecular weight polymers

The viscoelastic behavior of low molecular weight polymers exhibiting a fairly broad distribution has been deduced from the behavior of narrow samples by way of a linear law as a function of the density of the molecular weight distribution. Rheology of polydisperse linear polymers where the entire distribution of molecular weights is lower than 2 M _ehas been investigated using both binary mixtures and a broad sample of polystyrene. A decrease of the friction coefficient and of the viscosity compared to that of a narrow sample with the same M _w is observed. Therefore, the low components of broad samples play the role of plasticizers or lubricants which has been investigated in relation with the molecular weight distribution.     

Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution

A Hamiltonian framework of non-equilibrium thermodynamics is adopted to construct a set of dynamical continuum equations for a polymer blend with matrix viscoelasticity and a narrow droplet size distribution that is assumed to obey a Weibull distribution function. The microstructure of the matrix is described in terms of a conformation tensor. The variable droplet distribution is described in terms of two thermodynamic variables: the droplet shape tensor and the number density of representative droplets. A Hamiltonian functional in terms of the thermodynamic variables is introduced and a set of time evolution equations for the system variables is derived. Sample calculations for homogenous flows and constant droplet distribution are compared with data of a PIB/PDMS blend and a HPC/PDMS blend with high viscoelastic contrast. For the PIB/PDMS blend, satisfactory predictions of the flow curves are obtained. Sample calculations for a blend with variable droplet distribution are performed and the effect of flow on the rheology, droplet morphology, and on the droplet distribution are discussed. It is found that deformation can increase or decrease the dispersity of the droplet morphology for the flows investigated herein.     

Relaxational interactions and viscoelasticity of polymer melts. Part I: model development

Rheological equations of state for the concentrated solutions and melts of high polymers are derived by applying a structural approach. The dynamics of a macromolecule are considered on the basis of the fundamental model of the polymer chain, e.g., the bead-spring model. The drag forces describing correlations of motion macromolecules are determined by means of the relaxation equations. The oscillatory shearing flow of the melts is studied on the basis of the equations derived. Expressions for the dynamic modulus and relaxation times are determined. As can be judged from the form of the dependence of the dynamic modulus on frequency, the relaxation time distribution is the same as in real materials. The relaxation spectrum of high polymers has a terminal zone with abnormally long relaxation times.     

Experimental investigation of jets from rectangular six-lobed and round orifices at very low Reynolds number

This article presents an experimental study conducted on a six-lobed rectangular jet at a very low Reynolds number of 800. The near-exit flow dynamics is compared to the reference counterpart circular jet with same initial conditions. Flow dynamics is analyzed using time-resolved flow-visualizations, hot-wire anemometry and laser Doppler velocimetry. In the round jet, flow motion is dominated by large primary Kelvin–Helmholtz (K–H) structures. In the six-lobed rectangular jet, the K–H vortices are very thin compared to the large secondary vortices generated by the high shear at the lobed nozzle lip. The inspection of mean-velocity profiles and streamwise evolutions of the spreading rates in the major and the minor planes of the lobed jet confirm the absence of the switching-over phenomenon not observed on flow images. The streamwise structures that develop in orifice troughs render the volumetric flow rate significantly higher than that of the reference circular jet. Comparison of the obtained results to available data of the literature of similar rectangular six-lobed jets investigated at very high Reynolds numbers reinforces the notion that the three-dimensional flowfields at very low and very high Reynolds numbers are similar if the geometry of the lobed nozzle is conserved. However, important variations in flow dynamics might occur if one or several geometric parameters of the lobed nozzle are modified.