Frantisek Stepanek

New insights into the relationship between internal phase level of emulsion templates and gas–liquid permeability of interconnected macroporous polymers

Interconnected macroporous polymers can be made by polymerisation of emulsion templates consisting of an aqueous phase and a monomer phase (typically styrene and divinylbenzene) in which the aqueous (internal) phase is in the form of drops and the monomer phase is the continuous phase between the drops. Until recently it was thought that interconnected macroporous polymers could only be produced from the polymerisation of high internal phase emulsion (HIPE) templates with an internal phase level exceeding 74 vol%. Improvement of the poor mechanical performance, characteristic of such macroporous polymers, was achieved simply by increasing the material density of the macroporous polymer. However, this required a reduction in the internal phase volume of the emulsion template. Polymerisation of the continuous organic phase of emulsion templates with an internal phase volume ranging from 84 vol% to 70 vol% resulted in the production of poly(merised)HIPEs, polymerisation of medium internal phase emulsions with internal phase volume ranging from 70 vol% to 30 vol% in polyMIPEs and polymerisation of a low internal phase emulsion with an internal phase volume of 25 vol% in a polyLIPE. The resulting macroporous polymers were characterised in terms of mechanical and structural properties as well as gas and mercury permeability. Compression tests show that mechanical properties improved as the material density was increased. Gas and mercury permeability measurements show that as the internal phase volume of the emulsion template is reduced, the permeability of the resultant macroporous polymer is also reduced. However, surprisingly even macroporous polymers produced from low internal phase emulsion templates (25 vol%) were permeable with a gas permeability of 2.6 × 10−14m2 indicating that polyLIPEs are still interconnected macroporous polymers. Reconstruction modelling of the transport properties of porous materials shows that the permeability of a porous material with similar structures to that of the macroporous polymers increases exponentially with the porosity.

Multi-Scale Analysis of Vacuum Contact Drying

The modeling of the unit operation of vacuum contact drying is approached as a multi-scale problem. At the particle assembly length scale, effective transport properties (thermal conductivity, relative gas- and liquid-phase permeability) have been determined computationally by simulations on reconstructed porous media and verified by direct measurements. A distributed-parameter model of vacuum contact drying including liquid and vapor flow and differential energy balance has been formulated and used for the calculation of drying time as function of vacuum level, temperature, vessel diameter, and batch size at the unit operation length scale. Drying curves for a model system of sodium carbonate–isopropanol have been measured experimentally and compared with the model predictions. A very good agreement has been found.

AN OXYGEN TRANSPORT MODEL FOR HUMAN BONE MARROW MICROCIRCULATION

Human bone marrow (BM) is the site for haematopoiesis, or blood cell formation, and a tissue of complex architectural organization, whichh promotes the micro-environmental niches that regulate haematopoietic stem cell renewal and differentiation. Oxygen tension distribution is an important modulator of stem and progenitor cell proliferation and differentiation. Currently, it is impossible to measure oxygen tension levels in situ and their spatial distribution within tissues and organs. Hence, conceptual models have been routinely utilized as an attractive alternative to simulate the oxygen tension distribution. However, detailed analyses of transport properties in the marrow have been deficient, despite its important function. In this report, we present the development of a mathematical model that simulates oxygen transport from the sinusoids ( BM microcirculation ) to the surrounding extravascular space using an extension to the Krogh-type genre. Based on the characteristics of the BM physiology, the sinus and tissue oxygen tension profiles are obtained for various cases including single- and multi-vessel systems. Furthermore, the effect of pre-sinusoidal vessels (arterioles) in the vicinity of the sinusoids on oxygen tension distribution is investigated. The parameter values are based on human BM and the results are correlated with known physiological BM phenomena.

Multi-scale modelling of growing polymer particles in heterogeneous catalytic reactors

Publisher Summary This chapter discusses the problem of polyolefine particle morphogenesis in a heterogeneous gas or slurry catalytic reactor. A conceptual modeling approach is proposed, allowing for the multiple time- and length-scales on which polymerization processes typically occurs. Models of polymer growth and flow in the pores of a catalyst support, catalyst particle fragmentation, and the evolution of a polymer macro-particle are described as well as physical characteristics of key objects forming the particles. The length-scales involved in a typical heterogeneously catalyzed fluid-bed polymerization reactor. For example, the polymerization kinetics at the molecular level determines the polymer chain-length distribution, tacticity, branching, and composition, which determines the visco-elastic properties of a polymer melt and its melting temperature. The properties of molten and semicrystalline polymer together with the architecture of a catalyst support then determine the catalyst fragmentation mechanism, which in turn affects the structure of a growing polymer macro-particle, thus its heat- and mass-transfer characteristics.

Vacuum Contact Drying Kinetics: An Experimental Parametric Study

Abstract Vacuum contact drying kinetics of a model system consisting of nonporous glass beads and water has been experimentally measured on a laboratory scale. A methodology for determination of drying curves from experimental data in a statistically robust way has been developed. The effects of jacket temperature, head-space pressure, particle bed depth, vessel diameter, and particle size on drying rate during constant and falling rate periods have been studied. It was found that in the range of parameters investigated, drying rate does not depend on the means of realization of the driving force (by temperature or pressure); drying rate in the constant-rate period decreases with increasing bed depth while the overall heat-transfer rate increases due to increased surface area. A very strong dependence of drying rate and regime on particle size was observed; the constant-rate period disappeared for small particles.

Vacuum Contact Drying of Crystals: Multi-scale Modelling and Experiments

Abstract A methodology for multi-scale modelling of the unit operation of vacuum contact drying has been developed, with the aim of parameter transfer from the laboratory scale to the pilot-plant scale. Models at three hierarchical levels - (i) lumped-parameter model of the unit operation, (ii) distributed-parameter model of heat and mass transfer in a particle bed of given size and geometry, and (iii) particle-scale model of heat and mass transfer for the estimation of effective transport properties - have been formulated and solved. Experimentally measured drying rates in a laboratory-scale vacuum dryer have been analysed using volume-averaged temperature profiles evaluated from the continuum model, and the effective heat-transfer coefficients have thus been obtained.

Performance of integration schemes in discrete element simulations of particle systems involving consecutive contacts

In this investigation, which is a follow-up study extending earlier work (Kruggel-Emden, Sturm, Wirtz, & Scherer, 2008), a realistic assessment of the performance of integration schemes in systems of moving particles and consecutive contacts is conducted. Linear contact models are applied throughout this work as they allow for an analytical solution of consecutive oblique impacts. The many-particle systems considered are the discharge of particles from a hopper and particle movement in a shaken container. Results for many-particle systems are robust with respect to the applied integration method and step size once particle interactions are resolved with a sufficient number of steps. The integration schemes are also evaluated based on consecutive particle/wall contacts. Integration of consecutive contacts in a discrete element framework implies repeatedly solving non-continuous systems of differential equations. Various termination conditions for the normal force models and adaptive time stepping for one-step integration methods are investigated. The effect of softened contacts on particle trajectories is discussed. Based on these insights, recommendations for the most accurate integration schemes are made.

Discrete Element Methods for Large Scale Particle/Fluid Simulations

The time- and event-driven discrete element methods are more and more applied to realistic industrial scale applications. However, they are still computational very demanding. Realistic modeling is often limited or even impeded by the cost of the computational resources required. In this paper the time-driven and event-driven discrete element methods are reviewed addressing especially the available algorithms. Their options for simultaneously modeling an interstitial fluid are discussed. A potential extension of the time-driven method currently under development functioning as a link between event- and time-driven methods is suggested and shortly addressed.Copyright

Wall shear rate distribution for flow in random sphere packings.

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1< or =varphi< or =0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As varphi-->0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.

A conceptual model for oxygen transport in the human marrow

Abstract Human bone marrow (BM) is the site for haematopoiesis, or blood cell formation, and a tissue of complex architectural organisation, which promotes the micro-environmental niches that regulate stem cell renewal and differentiation. However, to date, detailed analyses of transport properties in the marrow have been deficient despite BMs important function. This paper proposes a conceptual physiological model, based on an extension of the Kroghian model, for the detailed analysis of mass transfer in the human bone marrow. The systems of equations represent a steady-state conjugated boundary value problem and computational methods were used to obtain the solution. Furthermore, novel techniques for the expansion of the model are also proposed.