Transport and structure formation process in suspension shear flows in the vicinity of rigid walls
Final Report Abstract
The object of this work was the investigation of the influence of solid, boundary walls in shear flows of suspensions. The development of a new phenomenological model describing the wall influence in a suspension was to be combined with an experimental investigation. In shear-flowing suspensions demixing processes and particle transport take place due to hydrodynamic diffusion. Particle-particle interactions lead to statistical fluctuations of the particle velocities. Gradients of the interaction frequency and viscosity gradients orthogonal to the flow direction might generate a systematic particle drift possibly leading to inhornogenities of the suspension and to a pseudo wall slip. The presence of a solid boundary wall also affects the shear-induced particle migration. Our approach is basing on the fact that the resistance force acting on particles very near the wall moving orthogonal to the wall is increased in comparison with the Stokes force. The new approximation of the resistance coefficient being a function of the distance to the wall leads to a a new diffusion equation including wall influence valid for a creeping flow of a suspension with spherical, monodispersely distributed particles neglecting the Brownian motion and inertia effects. A further addition is made taking into account sedimentation or buoyancy directed parallel to the particle drift. The resulting partial differential equation determines the particle concentration as a function of the time and the position in the flow accounting for wall influence and gravity. Herewith certain properties of suspensions under wall influence either analytically or numerically can be calculated. The particle concentration profiles, shear rate profiles and velocity profiles of half-infinite and two-wall Couette flows at steady state with and without gravity were determined as well as the start-up particle concentration development of a non-flowing suspension with one and with two walls experiencing gravity. Further wall effects were derived. The following results have been derived: In the Couette flow of a suspension at steady state the particle concentration near the wall is a monotone function that approximates zero at the wall and rises with increasing distance to the wall. The resulting boundary layer of low particle concentration at the wall leads to a pseudo wall slip. Even if gravity steers the particles towards the wall there is still a boundary layer containing few particles. At initial homogenous particle distribution the establishment of the boundary layer needs only a very low strain and happens thus very fast. The boundary layer becomes more narrow with increased average particle concentration. The existence of a pure fluid phase without particles depends on the mean particle concentration and on the difference of the densities of particles and fluid. The particle concentration profiles, shear rate profiles and velocity profiles in a Couette flow of a suspension at steady state without gravity scale with the particle size. During an experiment without gravity at a fixed initial particle concentration in a pure shear flow the particle concentration is dependant solely on the total strain and not on the occurring shear rates or shear stresses. In order to analyze the particle distributions in shear-flowing suspensions experimentally the method of nuclear magnetic resonance was employed basing on the detection of protons serving as sensors (H-NMR). Differing NMR signal intensities of matrix fluid and particles make it possible to distinguish the two phases. With regard to that a special shearing device realizing an oscillating tube flow of unlimited shearing time was designed and constructed. The oscillation of the tube flow does not affect the particle migration as for that the direction of the flow is irrelevant. After shearing the removable tube can be taken out and inserted into the nuclear magnetic resonance tomograph. The viscosity of the substance was high enough to prevent further rearranging of the particles during measuring time. The measured spin density distributions (corresponding to the particle distribution) of a suspension before and after shearing within the apparatus shows that during shearing the initially homogenous suspension the particles have accumulated in the center of the tube. At the tube wall the particle concentration is low in agreement with the theoretical results (pseudo wall slip). To find out NMR-specific artifacts appearing at the discontinuities of the spin density function the NMR signals of a pure solution and of a suspension in a tube were simulated. In addition the gravity-driven tube flow of a suspension containing an inbuild mechanical blending device was analyzed insitu by means of a hose leading directly through the NMR spectrometer. Spin density profiles and velocity profiles were measured. Both correspond to a demixing rendering a boundary layer of low particle concentration along the tube wall. Prom the velocity profiles shear rate profiles and viscosity profiles follow. Since the viscosity is a function of the particle concentration the particle concentration profiles can be determined. The particle concentration profiles determined from the spin density distribution agree well with the particle concentrations derived from the velocity profile. The flow behaviour of suspensions plays an important role in many areas of industry and daily life. Relevant macroscopical properties as pressure loss, volume flux, integral viscosity or residence times are determined by the local structure in the suspension. Hereby a present solid boundary wall leads to particle transport, structure formation or demixing and thus influences the macroscopical properties of the flowing suspension and therewith the efficiency of industrial processes and the quality of products. As an example the demixing of a suspension might be important if making a product by solidifying a suspension. If the product is to be desired homogenous a demixing has to be avoided, if the product is to be inhomogenous, a demixing might be desired and even useful.
Publications
- S. Muckenfuß, H. Buggisch Particle concentration in shear flow nearby the wall Chemie-Ingenieur-Technik 74, 956 (2002)
- S. Muckenfuß, H. Buggisch Shear flow of suspensions under wall Influence: Phenomenological theory and effects Proc. Appl. Math. Mech. 3, 414-415 (2003)
