Helical flow of molten polymers in a cylindrical annulus

Summary The paper is concerned with an analytical investigation of helical flow of a non-Newtonian fluid through an annulus with a rotating inner cylinder. The shear dependence of viscosity is described by a power law and the temperature dependence by an exponential function.Velocity and temperature profiles, energy input and shear along the stream lines, pressure drop, and torque are presented for the range of input parameters encountered in polymer extrusion.The results of the study can be applied to a mixing element in a screw extruder and for a device to control extrudate temperature and output.Nomenclature a thermal diffusivity [m²/s] - b temperature coefficient [K^–1], see eq. [4] - c heat capacity [J/kg K] - h slot width [m] - I ₁,I ₂,I ₃ invariants of the rate of deformation tensor, see eq. [5] - k thermal conductivity [J/m s K] - l, L = 1/h length of the slot - l _T ,l _K thermal and kinematic entrance length - m power law exponent, see eq. [3] - M torque [m N] - p pressure [N/m²] - P dimensionless pressure gradient, see eq. [24] - P _R,P _RZ dimensionless components of the shear stress tensor, see eq. [25] and eq. [26] - r, R = r/r _wa radial coordinate - r _wa, r_wi outer and inner radius of annulus [m] - t time [s]; dwell time in the annulus - T temperature [K] - v , v_r, V_z velocity components [m/s] - v ₀ angular velocity at inner wall [m/s] - average velocity inz-direction [m/s] - V , V_R, V_Z dimensionless velocity components,v /v₀, v_r/v₀, v_z/v₀ - V _z velocity ratio, helical parameter - Y coordinate inr-direction, see eq. [20] - z, Z = z/h Pe axial coordinate - deformation - rate of deformation tensor [s^–1] - apparent viscosity [N s/m²], see eq. [3] - dimensionless temperature,b (T – T ₀) - azimuth coordinate - ratio of radii,r _wi/r_wa - density [kg/m³] - , kl shear stress tensor [N/m²] - fluidity [m²w/Nw s], see eq. [4] - Gf Griffith number, see eq. [12] - Pe Péclet number, see eq. [13] - Re Reynolds number, - 0 initial state, reference state - equilibrium state - e entrance - wi, wa at surface of inner or outer wall - r, R, z, Z, coordinates - i, j radial and axial position of nodal point in the grid - k, l tensor components Presented at Euromech 37, Napoli 6. 20–23. 1972.With 15 figuresDedicated to Prof. Dr.-Ing. G. Schenkel on his 60th birthday     

On the problem of interfacial damage in fibre-reinforced composites under variable loads

In this paper, the theoretical background for the failure analysis of fibre-reinforced composites under variable repeated loads in the framework of direct methods is presented. It is based on a local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite.     

Turbulence structure of dilute polymer and surfactant solutions in artificially roughened pipes

Pressure drop and velocity profile measurements are presented for turbulent flows of drag reducing fluids. The investigation was done in two rough pipes, known as k- and d-type rough pipes. The results are compared with those obtained in hydraulically smooth pipe of identical diameter. The spatial arrangement of the roughness elements in the pipe determines the parallel shift in the elastic sublayer and in the core region of the dimensionless turbulent velocity profile. The slopes of the velocity profiles in these regions remain unaffected by the arrangement which is an indication that the hydrodynamic influence of the roughness is restricted to the near-wall region. The drag reducing surfactant solution exhibited a drag reduction in the smooth as well as in the rough pipes which was higher than that given by Virk's maximum drag reduction asymptote. For this solution no influence of the roughness on the turbulence was detected when the dimensionless roughness height in viscous units was less than 12.     

Analytical study of the interface in fibre-reinforced 2D composite material

Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures.An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibrereinforced composite materials are proposed.The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems.All solutions are obtained in a closed analytical form.The obtained results can be used for the calculation of pull-out and pushout tests,as well as for the investigation of the fracture of composite materials.     

Impact of sorption phenomena on multiphase conveying processes

Twin-screw multiphase pumps are employed increasingly to convey multiphase mixtures of crude oil, accompanying fluids, associated gas and solid particles. They are positive displacement pumps and suitable for handling products containing liquid accompanied by large amounts of gas. Experimental investigations on the conveying characteristic, namely measuring the delivered volume flow as a function of the pressure difference, provide results for selected mixtures. By means of the on hand work, the influence of sorption phenomena occurring due to pressure variations alongside the conveying process on the conveying characteristics of twin-screw pumps delivering mixtures of oil and gases is measured. The employed gases are air and carbon dioxide, which differ strongly in solubility in oil. All experiments are conducted in a closed loop test facility, where oil and gas volume flows are mixed before the inlet and separated after the outlet of the multiphase pump. In order to simulate the influence of the suction side pressure drop in the reservoir on the conveying characteristic, packed beds are employed as oil-filed model. Sorption processes inside of the oil-field model and within the multiphase pump affect the conveying behaviour significantly. The two-phase flow in the inlet and outlet pipe is visualised by means of a capacitance tomography system. Results show that the oil fraction of the total delivered volume flow is decreased due to desorption at the pump inlet. The gas fraction at the pump outlet is further decreased due to absorption. Experimental results are compared to calculated solubilities of the on-hand gases in oil and to the theoretically derived gas volume flow fraction expected at the multiphase pump.     

Spektroskopische Bestimmung der Doppelbindungslage in Phospholinen

Zusammenfassung Die Spin-Spin-Kopplungskonstanten der olefinischen Protonen mit dem ³¹P sowie die Feinstruktur der ¹H-NMR-Spektren sind charakteristisch für die Lage der Doppelbindung. Vielfach kann auch die Intensität der _C=C-Schwingung im IR zur Bestimmung der Doppelbindungslage benutzt werden. Massenspektren geben nur in Ausnahmefällen Hinweise, können jedoch zur exakten Bestimmung des Molekulargewichts dienen.

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Summary The spin-spin coupling constants of the olefinic protons with the phosphorus-31 as well as the fine structure of the nmr-spectra are characteristic for the position of the double bond. In the infrared, the intensity of the _C=C-frequency may often serve as indication of the position of the double bond. The applicability of mass spectra is limited to a small number of compounds. They may be used, however, for an accurate determination of the molecular weight.

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Die Ausführung der Untersuchungen erfolgte unter Mitarbeit von Herrn F. Dlugosch, Herrn H. Au und Fräulein R. Barth.

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Herrn Dr. C. A. Reilly, Shell-Development Company, Emeryville, USA, danken wir für die Überlassung getesteter Programmkartensätze zur Berechnung der NMR-Spektren.     

Two strained hexahelicenophanes

The crystal structures of the [6]­helicenes 4,13‐(1,10‐deca­methyl­ene­dioxy)­hexahelicene, C₃₆H₃₄O₂, (I), and 4,13‐(1,8‐octa­methyl­ene­dioxy)­hexahelicene, C₃₄H₃₀O₂, (II), show strong steric interactions between the terminal benzene rings and the poly­methyl­ene­dioxy chains. The shortest ring A and F distances amount to 2.941 (3) and 2.902 (3) Å, respectively. The increased steric energy of the ground state is responsible for a significantly lower racemization barrier of (I) and (II) in comparison to the unsubstituted [6]­helicene.     

Electrochemical etching of silicon carbide

Both n- and p-type SiC of different doping levels were electrochemically etched by HF. The etch rate (up to 1.5 μm/min) and the surface morphology of p-type 6H-SiC were sensitive to the applied voltage and the HF concentration. The electrochemical valence of 6.3 ± 0.5 elementary charge per SiC molecule was determined. At p-n junctions (p-type layer on a n-type 6H-SiC substrate) a selective etching of the p-type epilayer could be achieved. For a planar 6H-4H polytype junction (n-type, both polytypes with equal doping concentrations) the 4H region was selectively etched under UV illumination. Thus polytype junctions could be marked by electrochemical etching. With HCl instead of HF no etching of SiC occurs, but a SiO₂ layer (thickness up to 8 μm) is formed by anodic oxidation. Received: 29 October 1998 / Accepted: 27 January 1999