Hans Buggisch

The normal stress behaviour of suspensions with viscoelastic matrix fluids

Abstract We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented.

NMR imaging of pastes in a ram extruder

Abstract Nuclear magnetic resonance (NMR) imaging was used to investigate the extrusion behaviour of pastes with a ram extruder. Extrusions of limestone pastes with moisture contents of 23–29% and pastes of an oxide ceramic (Pural) with moisture contents of 72–76% have shown that NMR is a suitable method for the detection and quantification of structural changes and flow processes in pastes, e.g. the relative motion between the liquid and the solid phases, the beginning and time-dependent development of fissures within the cylinder filling and the extrudate, peptization and agglomeration. With NMR one can distinguish between free and bound water and determine the spatial distribution of the respective fractions of a phase within a specific volume element. Furthermore the time- and location-dependent displacement profiles of the solid and the liquid can be observed.

On the Modelling of the Electro-Hydrodynamic Flow Field in Electrostatic Precipitators

Electro-hydrodynamic (EHD) flows are investigated theoretically and numerically in this paper and results are presented for the flow field in model electrostatic precipitators (EPs). The resulting flow fields are shown in various representations and explained qualitatively. Numerical calculations with different flow models (non-turbulent and RANS) were conducted to investigate the influence of the flow model on the resulting secondary flows. Furthermore, a perturbation analysis is presented, leading to a simple differential equation of the Helmholtz type. This allows a more detailed view of the important mechanisms forming the secondary flows as well as being able to obtain a very fast estimation of the resulting flow field. The calculations reveal a strong influence of a vortex formation at the beginning of the precipitation zone on the whole flow field. Furthermore, a strong effect of the boundary conditions of the electric field and the operating parameters is shown.

Flow behavior of pastes with a deformation history dependent yield stress

Abstract A constitutive equation is introduced in order to describe hardening of oxide-ceramic materials subjected to simple shear flow. The material is modeled as a Bingham fluid with a yield stress that depends on the deformation history. This new material law is studied for several flow situations: simple shear flow between two parallel plates (induced via constant velocity motion of the plates relative to one another), pipe flow with a constant pressure drop, and flow through an acutely conical die at a given volumetric flow rate. For flow between parallel plates, the shear stress is examined as a function of the strain. In the case of pipe flow, the time dependent development of the velocity field and volumetric flow rate is determined. The pressure distribution obtained in flow through a rotationally symmetrical conical die is compared for two material classes: fluids with a constant yield stress versus those in which the yield stress depends on the deformation.

Low Reynolds number flow fields in imperfect fibre arrangements

Abstract In the first part a new theoretical approach is described, which yields an approximate analytical representation of the Stokes flow passing perpendicular through an isolated infinite grating of parallel, unequally spaced circular cylinders in a periodic arrangement. The method is based on a well-known analytical solution for the case of equidistant parallel cylinders and, moreover, on the Helmholtz minimum rate of dissipation theorem, for which an extended formulation is presented here. The analytical results are compared with velocity profiles and streamline patterns, calculated with the help of a commercial finite-element program. In the second part of this paper an experimental method is described, which allows the determination of the flow forces exerted on individual cylinders by measuring the elastic deflexions, the cylinders experience when being exposed to the flow. The theoretical and experimental results are compared. For the two-dimensional measurement of the deflexions, a new realization of the laser-triangulation technique is employed, whose absolute accuracy substantially surpasses that of conventional instruments.

Flow of newtonian/non-newtonian fluids in a bundle of tubes and in a packing of beads by MRI

The flow of newtonian fluids in packed columns (model filters) has been well investigated in the past, whereas there are deficits of knowledge about non-newtonian fluids, even though the filtration of such fluids commonly occurs in industrial processes. There is good knowledge about integral quantities (flow rate, pressure loss), but the velocity distributions depending on the geometry of the pore structure have not yet been investigated. The aim of our investigation is to find criteria for favorable pore structures (filter design). As a first step NMR-experiments on the flow of newtonian fluids and of shear-thinning xanthan gum solutions through single tubes and two-tube-systems have been performed, that permit the rapid determination of rheological properties without large experimental effort.

Wall Slip Behavior of Alumina-Silicone Oil Pastes During Extrusion

In this work, the applicability of two rheological characterization methods to determine the wall slip velocity during extrusion of alumina/silicone oil pastes has been examined. The results are compared with those obtained using another more recently developed technique called the color marking method. These methods were used to determine the wall slip behavior of model pastes as a function of solids concentration, shear stress and extrudate velocity.

Ein rheometer zur untersuchung von flüssigen polymermaterialien in einachsiger und zweiachsiger Dehnung

ZusammenfassungWir stellen ein neues Dehnrheometer vor, mit dem sowohl einachsige als auch zweiachsige Dehnexperimente an flüssigen Polymermaterialien durchgeführt werden können. Bei der Apparatur wird das Prinzip der „atmenden Blase” verwendet: Über eine Düse wird in das zu untersuchende Material eine kugelförmige Blase aus einer niederviskosen, inkompressiblen, unmischbaren Flüssigkeit injiziert. Wachstum bzw. Schrumpfen dieser Blase führt zu einer zweiachsigen bzw. einachsigen Dehndeformation der umgebenden Polymerflüssigkeit. Der Injektionsdruck dient als Meßgröße zur Bestimmung der viskoelastischen Eigenschaften des Probenmaterials. Bei vergleichsweise niederviskosen Silikonölen gelingt die Messung der Nullviskosität bzw. der linear viskoelastischen Eigenschaften in guter Übereinstimmung mit Scherexperimenten. Bei Materialien mit ausgeprägt nichtlinear viskoelastischem Verhalten kann unter Anwendung des Wagner-Modells die Dämpfungsfunktion für ein- und zweiachsige Dehnung ermittelt werden. Unsere Ergebnisse für das Polyisobutylen Oppanol B 15 stimmen mit Messungen von Demarmels und Meißner überein, die mit der Methode der „Rotierenden Klemmen” durchgeführt werden. Für drei Polyisobutylene unterschiedlichen Molekulargewichts ergibt sich im Rahmen der Meßgenauigkeit die gleiche Dämpfungsfunktion.AbstractWe present a novel elongational rheometer for uniaxial and equibiaxial extension of polymeric liquids. The apparatus makes use of a growing or collapsing spherically symmetric bubble surrounded by a large amount of the polymeric liquid to be measured. The bubble is generated by injection of a low-viscosity immiscible liquid. The injection pressure is measured with the deformation rate of the bubble surface prescribed. The method is capable of reproducing the Newtonian viscosity and the linear viscoelasticity of comparatively low molecular weight silicone oils in excellent agreement with shear measurements. For materials strongly behaving nonlinear viscoelastically, we calculate Wagners damping function. Our results agree well with measurements made by Demarmels and Meißner using the rotary clamp technique for the polyisobutylene melt Oppanol B 15. Within the range of experimental and calculatory incertainties we find the same damping function for three polyisobutylenes of different molecular weights.

An exact solutions of a viscoelastic ekman layer with suction

Abstract Because of the higher order derivatives the second-order fluid model requires an additional boundary condition in some flow fields. In this paper we discuss the problem of the missing boundary condition by solving the Ekman layer with suction for two types of constitutive equations. In the case of a viscoelastic fluid model of integral type (see eqn. 25) we obtain a “well-posed problem” with an exact unique solution. In the case of a second-order fluid model (see eqn. 16) we encounter the problem of the missing boundary condition. For weakly non-Newtonian second-order fluids with eqn. (25) as the original (generating) equation this difficulty can be avoided by iteration, obtaining an asymptotic solution. This procedure can be applied only if the “second-order fluid approximation” holds true in the whole flow field.

Determination of the Power Law Exponent from Magnetic Resonance Imaging (MRI) Flow Data

To visualize the principle of flow imaging, MRI experiments were performed on laminar flow through simple geometry such as a single tube and a two-tube-system. Water is used as Newtonian fluid, shear thinning the Xantham gum solution as non-Newtonian fluid. The experiments allow the rapid determination of rheological properties of complex fluids.