Dynamical density functional theory for the diffusion of injected Brownian particles

While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly interacting Brownian particles. Dynamical density functional theory (DDFT) for classical Brownian particles represents an ideal tool for this purpose. After outlining the basic ingredients to DDFT we show that it can be readily applied to flowing suspensions with time-dependent particle sources. Particle interactions lead to considerable layering in the mean density profiles, a feature that is absent in the trivial case of noninteracting, freely diffusing particles. If the particle injection rate varies periodically in time with a suitable frequency, a resonance in the layering of the mean particle density profile is predicted

Liquid pair correlations in four spatial dimensions: Theory versus simulation

Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the Ornstein-Zernike equation, by comparing the results to computer simulation data. Our results are of relevance to understand crystal and glass formation in high-dimensional systems

Analytical growth equations and their Genstat 5 equivalents

Two ways of representing some of the existing growth functions, (the exponential, the monomolecular or Mitscherlich, the logistic or autocatalytic, the Gompertz, and the Richards equations) are compared. In the first, growth is expressed in the parameters mass at time zero W0, mass at time infinity Wf, and a measure for the relative growth rate k. In the second, different parameters are used because of robust parameter optimization (e.g., by the statistical software package Genstat). The relationships between these fitted parameters and the parameters W0, Wf and k are demonstrated. The properties of these models, such as physical meaning of the parameters, properties at the point of inflection (if it exists), and the growth rate at a limit W -> 0, are examined. The second order exponential polynomial was rewritten in such a way that use was made of a proportionality constant, equal to the relative growth rate at the point of inflection. Application of the growth models is demonstrated using data for lettuce grown in a nutrient film system. Finally, it is shown that, except for the exponential polynomial, all growth equations originate from one single equation

Electrokinetic and hydrodynamic properties of charged-particles systems: From small electrolyte ions to large colloids

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics

Waar en wat meten met sensoren in een substraat?; modelverkenning naar geschikte meetvariabelen en meetplekken in een zandbed- en steenwolteeltsysteem in de glastuinbouw

In gesloten, recirculerende teelten op substraat zijn de omstandigheden in de wortelzone goed onder controle te houden. De hoeveelheid, frequentie en manier van fertigeren kan gebruikt worden om de omstandigheden in de wortelzone te sturen. Daarvoor moeten de omstandigheden wel goed gemeten worden. De vraag is echter waar en wat er gemeten moet worden in een teeltsysteem. Modelberekeningen met het simulatiemodel FUSSIM2 laten zien dat het meten van het elektrisch geleidingsvermogen in de buurt van deplant het meest geschikt is om de omstandigheden te beoordelen. Met een berekening is aangetoond dat het mogelijk is om fertigatie te sturen op basis van de waarde van het elektrisch geleidingsvermogen gemeten op een plaats in het teeltsysteem