Feist, M. (KIT): Sedimentation and separation behaviour of fibre-particle syspensions

For many industrial applications like purification of waste water, some filtration processes and the paper recycling process, knowledge about the sedimentation and separation behaviour of fibre-particle suspensions is required to adjust processes and to gain best production results. In general, sedimentation processes are influenced by lots of parameters, like the material, the concentration or the inter-particle forces. In case of long particles, like fibres, an additional parameter, the form of the particle, has to be considered. It is well known that fibres tend to form clusters during sedimentation and that in a steady process fibres join and leave those clusters. In fibre-particle suspensions or in case of the purification of fibre-suspensions, particles or impurities get enclosed and therefore are withdrawn with the fibres and cannot be separated. So a detailed understanding of the kinetic of the fibre movements is necessary to influence the process. In this presentation we will first present experimental results, which show how different the sedimentation of fibre and-particle suspensions are in comparison to pure fibre or pure particle suspensions. We will show, how the kinetic of fibres come into consideration. Additionally we will introduce the model of the Stokesian Dynamics Method. With this method we are able to investigate the kinetics of fibre-particle sedimentation processes as well as their separation behaviour. Finally, we investigate the sedimentation behaviour of fibre- particle suspensions to show the influence of the density ratio between the fibres and particles and the length of the fibres on the separation behaviour.

Glusa, Chr. (KIT): Sedimentation in periodic domains

We want to model the settling behaviour of rigid spherical particles in fluid at low Reynolds number. As the hydrodynamic interactions between particles are of long range, we consider this problem on a periodic elementary cell. We derive slowly converging sums for the Green's function and use Ewald summation in order to accelerate the summands' decay. We briefly expose techniques that can be used for efficient implementations. This report aims to expose the different approaches found in literature, while giving a common notation and filling the gaps which arise sometimes in the methods' derivation.

Guazzelli, E. (Aix-Marseille Univ.): Falling clouds of particles

The time evolution of clouds of particles settling under the action of gravity in an otherwise pure liquid is investigated both experimentally and numerically. It is found that an initially spherical cloud containing enough particles is unstable even in the complete absence of inertia. The cloud slowly evolves into a torus which breaks up into secondary droplets which deform into tori themselves in a repeating cascade. The discrete nature of the particles is fundamental in the understanding of these instabilities. Faster breakup is observed for clouds of anisotropic particles such as fibers due to the self motion of the anisotropic particles. When inertia is finite, the cloud also deforms into a flat torus that eventually destabilizes and breaks up into a number of secondary droplets. While this behavior bears some similarity with that observed at zero-inertia, the underlying physical mechanisms differ. Moreover, the evolution of the cloud deformation is accelerated as inertia is increased. Two inertial regimes where macro-scale inertia and micro-scale inertia become successively dominant are clearly identified.

John, V. (FU Berlin): Numerical Methods for the Simulation of Population Balance Systems

Numerical simulations of population balance systems face several challenges:

• the equations for flow, energy, and concentrations are convection-dominated, sometimes also reaction-dominated,
• the systems couple equations that are defined in domains with different dimensions,
• some equations are integro-partial differential equations, where the efficient numerical evaluation of the integral terms requires special numerical schemes.

During the past years, our group has been considered several applications that lead to population balance models. The talk gives an overview on the numerical methods for population balance systems that have been studied. Most of them are based on finite element methods. Our experience with the used schemes concerning their applicability for the simulation of population balance systems will be discussed.

Keller, F. (KIT): Primary charge effects on prolate spheroids with moderate aspect ratios

Colloidal particles, i. e., particles with a size below 1 μm, play an important role in chemical, biological, and environmental engineering. Especially, anisotropic particles have come into the focus of the current research due to their potential applications in paints, ceramics, and photonic materials. Moreover, they play also an important role in biological processes, since, e. g., bacteria, viruses, and DNA fragments can be modeled as rod-shaped colloidal particles. The transport properties of these particles, like their sedimentation velocity and their rotational and translational diffusion coefficients, give information about the particle size and their anisotropy. However, since colloidal particles in aqueous electrolyte solutions normally acquire a non-zero surface charge, electric double layers around the particles develop, which finally alter their behavior. Therefore, it is crucial to understand the effects of the double layer on the transport properties of anisotropic particles.

In this talk, we consider the effects of an ambient fluid flow, namely a uniform incident flow field and a shear flow, on a charged spheroidal particle with surrounding electric double layer. We especially extend the results known in the literature to the case of prolate spheroids with moderate aspect ratios, where the assumptions of the slender-body theory fail and end-effects have to be taken into account. Therefore, it is necessary to consider the Stokes–Poisson–Nernst–Planck system that has to be solved numerically. For the numerical simulations, we use the finite element method and propose an efficient semi-implicit time-discretization based on a splitting of the Stokes equation. For low Reynolds numbers, we find approximating linear expressions between the ambient fluid flow and the force and torque on the particle. The description of this linear behavior is based on the resistance functions, whose dependencies on the Debye length and the zeta potential will be investigated.

Marheineke , N. (Erlangen): Asymptotic and stochastic surrogate models for fiber-fluid interactions

The production process of technical textiles rises exciting challenges in mathematical modelling, numerical simulation and optimization of fiber-fluid interactions. In the process, hundreds of individual fibers are obtained by a continuous extrusion of a molten granular through narrow nozzles. They are stretched and entangled by acting turbulent air flows to form a three dimensional texture, while laying down on a moving conveyor belt. The technical textiles find their application in various branches of industry, e. g. in textile, hygiene, automobile and building industry. Typical products are clothing textiles, baby diapers, oil and water filters, sound proofing, insulating material etc. Depending on their use, the textiles have to satisfy certain properties. An important common property for the quality assessment of the fabrics is the homogeneity of the fiber web.

The production process might be considered as a multiphase problem, i. e. slender visco-elastic polymer jets in interaction with a turbulent air flow in a highly complex geometry. The uniform treatment of this multiscale problem is not possible due to the enormous computational effort. Therefore, in this talk a model-chain is presented that consists of appropriate mathematical models for single aspects being coupled via asymptotic analysis, similarity estimates, parameter identification and stochastic surrogates. The chain enables the simulation of the process and even more the prediction of certain material properties. The models range from a complex three-dimensional fluid-solid problem with slender bodies in turbulent flows to asymptotic Cosserat string models for the fiber dynamics with stochastic aerodynamic drag forces and and further to efficiently evaluable stochastic surrogate models for the fiber lay-down.

Prignitz, R. (Erlangen): Particulate Flows with the Subspace Projection Method

A method is presented for the simulation of viscous incompressible flow with many suspended solid particles. This method uses a finite-element discretisation in space and an operator-splitting technique for discretisation in time and has its basis in work by Glowinski et al.
However, a subspace projection rather than a Lagrange multiplier is used to couple the particle motion with the fluid motion.

Combined with local mesh refinement the method results in a fast and accurate algorithm for the simulation of a huge number of particles in a flow field. Validation is achieved using the sedimentation of one particle and comparing the resulting drag coefficient with theoretical and experimental results.

Uhlmann, M. (KIT): Turbulence interacting with finite-size particles

The interaction between turbulent flow and suspended solid particles is of interest in a considerable number of technical applications (e. g. civil and chemical engineering, combustion) as well as natural processes (meteorology, blood flow). However, such multi-phase systems are notoriously resistant to modeling while posing severe challenges to experimental and numerical approaches.

In recent years it has become feasible to simulate the motion of a growing number of resolved particles, including an adequate description of the near-field. Although system sizes are still limited, this fully-resolved approach to direct simulation of particulate flow is starting to produce physically significant results.

In the present contribution we will discuss recent simulations of turbulent channel flow seeded with particles having a diameter corresponding to 11 viscous wall units. We will focus on the discussion of the disperse phase geometry, on particle acceleration statistics and particle-conditioned averaging.