De transport- en overdrachtsprocessen van warmte, massa en impuls worden naar hun analogie behandeld. De processen worden beschreven met behulp van macro- en microbalansen die in veel gevallen leiden tot differentiaalvergelijkingen. Ook veel aspecten van stromingsleer komen op deze manier aan de orde en zo bereidt het boek ook voor op moderne Computational Fluid Dynamics technieken. Het doel van het boek is ook studenten te trainen in het oplossen van problemen waarbij transportverschijnselen centraal staan. Daartoe bevat het boek bijna 100 uitgewerkte vraagstukken.

The intermolecular interactions in the pseudo-potential lattice Boltzmann (PPLB) method can readily be extended to more than two components. We report about a three-component PPLB approach to explore whether the effect of a surfactant could be included in describing droplet behaviour in (liquid–liquid) emulsions. The two main liquid components are taken to follow the Carnahan-Starling equation of state (EoS), while the surfactant obeys an ideal EoS. We investigate the nature of the phases present at equilibrium and the dependence of the interfacial tension between the two liquid phases on the amount of surfactant. The response of a droplet subjected to simple shear is investigated in the absence and the presence of a surfactant. Our exploratory simulations show how during droplet deformation the surfactant re-distributes itself due to the action of the shear and flows towards the far ends of the deformed droplet, up to the moment the droplet breaks up. This inhomogeneous surfactant distribution along the interface increases the shear rate that is needed for droplet breakup such that the critical capillary number for breakup increases and the breakup process is delayed. The simulations also reveal the detailed flow fields inside and outside the deforming droplet.

Computational Fluid Dynamics (CFD) is exploited to study mass transfer in a specific stirred aerated bioreactor used in a cell culture process. The focus is on which empirical correlations from the literature can best be used for calculating the volumetric mass transfer coefficient kLa on the basis of the spatially distributed and/or average energy dissipation rate obtained in CFD simulations. This energy dissipation rate plays a key role in many of the empirical correlations which are reviewed in detail. CFD simulations are carried out using the finite volume (FV) ANSYS Fluent software as well as the Lattice Boltzmann (LB)-based code marketed by M−Star. In Fluent, we opted for a two-fluid approach and the realizable k-ε turbulence model, while M−Star models the turbulence by a Large Eddy Simulation and tracks individual bubbles in a Lagrangian way. Gassed power draw, air volume fraction, energy dissipation rate, and (kLa) are calculated in both codes and compared mutually as well as to experimentally measured data and analytical correlations available in the literature. The energy dissipation rate was underpredicted by Fluent, leading to lower breakup rates and an underprediction of kLa. The M−Star simulations also underpredict kLa although predicting much higher levels of energy dissipation. However, using a constant value for kL and just the volume-averaged a from Fluent or M−Star improved the results significantly, which then are in good agreement with the experimental kLa value.

Deze vraagstukkenbundel is bedoeld als oefenmateriaal bij het bestuderen van de basiscolleges Fysische Transportverschijnselen, zoals die aan de TU Delft worden gegeven. De vraagstukken zijn afkomstig uit oude vraagstukkenbundels en uit recente tentamens. Wij hebben de formulering van veel van deze vraagstukken herzien.

Vooral door de vraagstukken in meerdere onderdelen te splitsen, hopen we aan te geven dat een stapsgewijze aanpak, veelal gebaseerd op één of meer balansen, een bruikbaar recept voor het oplossen van de opgaven is. Overigens is deze splitsing bij lang niet alle opgaven doorgevoerd om aan studenten de gelegenheid te geven juist dit moeilijke facet zelf te oefenen.

The development of a novel numerical model for droplet drying is the topic of this paper. The three main stages of droplet drying are distinguished, viz. unhindered evaporation of a ’wet’ particle (the droplet), restricted drying at a falling rate due to the formation of a crust around a wet core, and inert heating of the dry porous particle. Each stage is mathematically detailed to replicate all phenomena occurring throughout the drying process. The focus, however, is on the falling rate drying regime which is described in terms of Stefan diffusion of water vapour through the pores of a thickening crust. To this end, the model needs the material properties. This permits the droplet characteristics to be determined by composition rather than through single-droplet drying experiments. Finally, the model is validated against five of such experiments from literature using skim milk. Good agreement is found at each comparative case for the particle mass and temperature throughout the various drying regimes providing that for good reasons in three cases a lower drying air temperature is applied than reported for the experiments. The model is capable of predicting the entire drying process at low computational cost and without requiring empirical input.

We carried out 3D simulations of monodisperse particle suspensions subjected to a constant shear rate with the view to investigate the effect of electrical double layers around the particles on apparent suspension viscosities. To this end, expressions for Debye length, zeta potential, and ionic strength (pH) of the liquid were incorporated into our in-house lattice Boltzmann code that uses the immersed boundary method and includes subgrid lubrication models. We varied the solids concentration and particle radius, keeping the particle Reynolds number equal to 0.1. We report on results with respect to the effect of pH in the range 9 through 12 and of Debye length on apparent viscosity and spatial suspension structures, particularly at higher solids volume fractions, and on the effect of flow reversals.

We report the findings of a detailed assessment of various options for computational two-fluid RANS simulations of an aerated agitated 2-L bioreactor equipped with a single baffle and several dip tubes. The simulations were carried out by using the commercial flow solver ANSYS/Fluent. Our focus was on (1) the outlet condition at the liquid's surface (i.e., including an air head space in the simulation yes or no); (2) the choice between the steady-state Multiple Reference Frames (MRF) approach for modelling the impeller rotation and the dynamic Sliding Mesh (SM) option; (3) the choice between two computational meshes (mosaic or polyhedral); and (4) the effect of using either the realizable k-ε model or the SST k-ω model for dealing with the turbulence in combination with different values for the fixed bubble size (either 1.8 or 2.8 mm). The final conclusion is that the SM impeller model in combination with a polyhedral computational mesh and the SST k-ω turbulence model is to be preferred. All simulations suffer from the occurrence of spurious velocities larger than the impeller tip velocity.

A treatment of the transport and transfer processes of heat, mass and momentum in terms of their analogy. The processes are described with the help of macro and micro balances which in many cases lead to differential equations. This way, the textbook also prepares for Computational Fluid Dynamics techniques. The topics of the five chapters of the textbook are: • Balances: shape and recipe, mass balance, residence time distribution, energy and heat balances, Bernoulli equation, momentum balances • Molecular transport, dimensional analysis, forces on immersed objects • Heat transport: steady-state and unsteady conduction, the general heat transport equation, forced and free convective heat transport, radiant heat transport • Mass transport: steady-state and unsteady diffusion, the general mass transport equation, mass transfer across a phase interface, convective mass transport, wet bulb temperature • Fluid mechanics: flow meters, pressure drop, packed beds, laminar flow of Newtonian and non-Newtonian fluids, Navier-Stokes equations The leading idea behind this textbook is to train students in solving problems where transport phenomena are key. To this end, the textbook comprises almost 80 problems with solutions. • Retaining the analogy between mass, heat and momentum transport • Using the technique of drawing up balances throughout the book • Suitable for a single term course.

De transport- en overdrachtsprocessen van warmte, massa en impuls worden naar hun analogie behandeld. De processen worden beschreven met behulp van macro- en microbalansen die in veel gevallen leiden tot differentiaalvergelijkingen. Ook veel aspecten van stromingsleer komen op deze manier aan de orde en zo bereidt het boek ook voor op moderne Computational Fluid Dynamics technieken. Het doel van het boek is ook studenten te trainen in het oplossen van problemen waarbij transportverschijnselen centraal staan. Daartoe bevat het boek bijna 100 uitgewerkte vraagstukken.

This contribution to the journal issue commemorating Professor Robert Byron Bird focuses on his Dutch connection, which dates back to as early as 1950. Bird twice spent a semester-long period at (the current) Delft University of Technology. The development over time of two different schools of teaching transport phenomena and their mutual influencing are reviewed in quite some detail. The cornerstone in both schools is the analogy between the transport modes for mass, momentum, and energy. However, the role of fluid mechanics and its treatment is different. In addition, the didactic concepts underpinning the textbooks from the two schools are rather different as well, both having their pros and cons. This is illustrated for the mechanical energy balance and its derivation.