Piet D. Iedema

Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor

SUMMARY A detailed comparison between the finite element method (FEM) and the lattice-Boltzmann method (LBM) is presented. As a realistic test case, three-dimensional fluid flow simulations in an SMRX static mixer were performed. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used as a highly efficient chemical reactor for viscous systems like polymers. The complex geometry of this mixer makes such three-dimensional simulations non-trivial. An excellent agreement between the results of the two simulation methods was found. Furthermore, the numerical results for the pressure drop as a function of the flow rate were close to experimental measurements. Results show that the relatively simple LBM is a good alternative to traditional methods. Copyright

No-slip boundary condition in dissipative particle dynamics

Dissipative Particle Dynamics (DPD) has, with only a few exceptions, been used to study hydrodynamic behavior of complex fluids without confinement. Previous studies used a periodic boundary condition, and only bulk behavior can be studied effectively. However, if solid walls play an important role in the problem to be studied, a no-slip boundary condition in DPD is required. Until now the methods used to impose a solid wall consisted of a frozen layer of particles. If the wall density is equal to the density of the simulated domain, slip phenomena are observed. To suppress this slip, the density of the wall has to be increased. We introduce a new method, which intrinsically imposes the no-slip boundary condition without the need to artificially increase the density in the wall. The method is tested in both a steady-state and an instationary calculation. If repulsion is applied in frozen particle methods, density distortions are observed. We propose a method to avoid these distortions. Finally, this method is tested against conventional computational fluid dynamics (CFD) calculations for the flow in a lid-driven cavity. Excellent agreement between the two methods is found.

CFD calculation of laminar striation thinning in static mixer reactors

A new method to calculate the average value of the rate of striation thinning, α, from the laminar flow field in a static mixer as simulated by Computational Fluid Dynamics (CFD) has been developed. The shape of the developing striations is inferred by executing a particle tracking procedure to the CFD flow field obtained. Problems arising from the complex trajectories and their translation to Ottinos (The Kinematics of Stretching, Chaos and Transport, Cambridge University Press, Cambridge, UK, 1989) micromixing theory have been solved. The method has been applied to mixer configurations with Kenics and SMX elements. Laser induced fluorescence experiments showed good agreement to model results when visually comparing the striation distribution patterns. The distribution of α values throughout the mixer could thus be calculated. The average value of α turns out to be constant per element. We have thus demonstrated that a micromixing theory could be adequately coupled to the accurate description by CFD of the flow pattern inside a reactor with local resolution.

State multiplicity in CSTR-separator-recycle polymerisation systems

Abstract This article continues earlier work (Comput. Chem. Eng. 24 (2000) 209) concerning the design and control of isothermal reactor–separator–recycle systems. The multiplicity behaviour of six reaction systems of increasing complexity, from one-reactant, first-order reaction to chain-growth polymerisation, is investigated. Below a critical value of the plant Damkohler number, Da Dacr. For one-reaction systems, one stable steady state is born at a transcritical bifurcation. For consecutive-reaction systems, including polymerisation, a fold bifurcation can lead to two feasible steady states. Moreover, the transcritical bifurcation is destroyed when two reactants are involved. If the gel-effect is included, a maximum of four steady states are possible. When multiple steady states exist, the achievable conversion is constrained by the instability of the low-conversion branch. This has practical importance for polymerisation systems when the radicals’ quasi-steady state assumption is not valid or the gel effect is significant.

Nonlinear behavior of reactor—separator—recycle systems

The nonlinear behavior of reactor—separator—recycle systems is studied. The dimensionless mole-balance equations are parameterized by the plant Damkohler number (Da) and the separation specifications. Reactant accumulation does not occur if Da > Dacr. DaCr corresponds to a bifurcation point of the mole-balance equations and depends on separation performance. For one reactant recycle and high purity separation, Dacr = 1. When two reactants are recycled, multiple steady states are possible. In this case, Dacr depends also on the control structure. Close to Dacr, control structures must change the reaction volume or temperature in order to reject effectively the disturbances.

Modelling multi-viscosity systems with dissipative particle dynamics

Dissipative particle dynamics (DPD) is a particle-based simulation technique. It is applicable on time and length scales in-between those typical for molecular modelling and continuum mechanics. These features make DPD an interesting tool in the area of multiphase flows. So far, multiphase DPD simulations were restricted to fluids with the same viscosity, because it was unclear how one could model phases with a different viscosity together. Here, we show how to deal with more than one viscosity in the system. The viscosity of a DPD fluid can be controlled with the friction factor, an input parameter in DPD that characterises the strength of the drag force between interacting particles. So, in a multiphase system each fluid has its own friction factor, yielding the viscosity of that fluid. Now, the problem is to define the friction factor for the interaction between particles of unlike fluids. This factor has a significant effect on flow dynamics, but lacks a related physical property such as interfacial tension or solubility to specify its value. Three methods are presented to calculate the friction factor between particles of unlike fluids. One of these methods only involves the friction factors of the individual fluids and is of most practical use in real applications. The methods are validated for steady and unsteady flow of two adjacent immiscible fluids. Results from these two-phase test cases are consistent with theory. This opens the door to more extensive modelling of multi-viscosity systems with DPD.

State multiplicity in PFR–separator–recycle polymerization systems

Abstract This article explores the non-linear behaviour of isothermal and non-isothermal plug-flow reactor (PFR)–separator–recycle systems, with reference to radical polymerization. The steady-state behaviour of six reaction systems of increasing complexity, from one-reactant first-order reaction to chain-growth polymerization, is investigated. In PFR–separator–recycle systems feasible steady states exist only if the reactor volume exceeds a critical value. For one-reaction systems, one stable steady state is born at a transcritical bifurcation. In case of consecutive-reaction systems, including polymerization, a fold bifurcation can lead to two feasible steady states. The transcritical bifurcation is destroyed when two reactants are involved. In addition, the thermal effects also introduce state multiplicity. When multiple steady states exist, the instability of the low-conversion branch sets a lower limit on the conversion achievable at a stable operating point. A low-density polyethylene process is presented as a real plant example. The results obtained in this study are similar to CSTR–separator–recycle systems. This suggests that the behaviour is dictated by the chemical reaction and flowsheet structure, rather than by the reactor type.

Using molecular weight distributions to determine the kinetics of peroxide-induced degradation of Polypropylene

The kinetics of peroxide-induced degradation of Polypropylene have been determined by comparing full molecular weight distributions from size exclusion measurements (SEC) to rigorously modeled ones. The basic idea is the unique effect of each mechanism on the shift in MWD. The existence of termination by disproportionation and transfer to polymer could thus be assessed, turning out to be highly coupled. The impact of residence time distribution and imperfect mixing on the MWD shift has been examined. The application of a straightforward mixing model suggests such effects to be non-important.

An infrared spectroscopic study of the nature of zinc carboxylates in oil paintings

The formation of metal soaps is a major problem for oil paintings conservators. The complexes of either lead or zinc and fatty acids are the product of reactions between common pigments and the oil binder, and they are associated with many types of degradation that affect the appearance and stability of oil paint layers. Fourier transform infrared spectroscopy (FTIR) reveals that a paint sample from The Woodcutter (after Millet) by Vincent van Gogh contains two distinct zinc carboxylate species, one similar to crystalline zinc palmitate and one that is characterized by a broadened asymmetric stretch COO− band shifted to 1570–1590 cm−1. This observation has been made in many paintings. Although several hypotheses exist to explain the shifted broad carboxylate band, these were not supported by experimental evidence. In this paper, experiments were carried out to characterize the second zinc carboxylate type. It is shown that neither variations in the composition of zinc soaps (i.e. zinc soaps containing mixtures of fatty acids or metals) nor fatty acids adsorbed on pigment surfaces are responsible for the second zinc carboxylate species. X-Ray diffraction (XRD) and FTIR analysis indicate that the broad COO− band represents amorphous zinc carboxylates. These species can be interpreted as either non-crystalline zinc soaps or zinc ions bound to carboxylate moieties on the polymerized oil network, a system similar to ionomers. These findings uncover an intermediate stage of metal soap-related degradation of oil paintings, and lead the way to improved methods for the prevention and treatment of oil paint degradation.

A comparison between lattice-boltzmann and finite element simulations of fluid flow in static mixer reactors

We present a comparison between the finite-element and the lattice-Boltzmann method for simulating fluid flow in a SMRX static mixer reactor. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used in highly efficient chemical reactors for viscous systems like polymers. The complex geometry of this mixer makes such 3D simulations nontrivial. An excellent agreement between the results of the two simulation methods and experimental data was found.