The salinity profile in a coastal sea-river system is the result of balancing of salt transport due to mixing of the water by tides and the freshwater discharge from the river. When for example during times of drought freshwater discharge suddenly declines, the salinity in the river may increase significantly and threaten drinking water supplies and agriculture. The time it takes for the salinity to reach the new equilibrium may be considerable. Thorough understanding of the adaptation process is essential for taking appropriate prevention measures. However, much about this adjustment process is still unknown, in particular regarding the interaction between the river and the adjacent sea. In this study, a simplified linear model is developed to describe a well-mixed river and the adjacent sea where the water flows radially away from the mouth of the river. The unique assumptions, most notably a time-independent intrusion length, allow for a unique analytical approach using the method of eigenfunction expansion. The smallest eigenvalues are found to define a time scale of the adjustment process. The eigenfunctions provide insight about how the salinity adjustment time varies within the system. The adjustment time does not only depend on the parameters that describe the new equilibrium, but also on the initial salinity. The eigenvalue time scales corresponding to the sea and to the river can then be used to determine the time scale of the coupled system. It is found that when the sea adjusts much faster than the river, the time scale of the river is leading the adjustment. When the eigenvalue time scale of the sea is similar to or larger than the eigenvalue time scale of the river, the adjustment time is significantly increased by the sea. When salinity is increasing, the sea restricts the inflow of salt in the river, while for decreasing salinity, the sea keeps transporting salt to the river by mixing which delays the adjustment. The model is applied to analyse a sudden decrease in freshwater discharge in the Rotterdam Waterway, which is part of the Dutch Rhine-Meuse delta. Results show that the salinity response is delayed compared to freshwater discharge, indicating that the adjustment time of the river indeed plays an important role. Further research should consider a more general dispersion relation or an extra vertical dimension to better describe estuaries that are not well-mixed. Using numerical methods there are many other possibilities to extend the model. The effect of tides on the presence and dynamics of the fresh water bulge in the sea is of specific interest.

Hot water pumped out of the ground for purposes of geothermal energy extraction cools down after it is used in a heat exchanger. The now cold water contains minerals that undergo a shift in chemical equilibrium. This may cause the minerals to come out of solution and become sediments. When pumping the cold water back into the porous ground, these sediments can cause cloggings that eventually lead to a net energy loss using this source. It will requiremore mechanical energy to pump up the water, than we gain in geothermal energy. In this reportwe aimto create a simple computer programthat models the creation of these sediments. The goal is to knowwhat minerals cause cloggings, and which do not. The program approximates the underground as a 0-dimensional tank with inflow and outflow called a Continuously Stirred Tank Reactor (CSTR).We derive a set of differential equations for both the inflow and outflow and the chemical reactions that take place. The chemistry used in this model uses data from individual reactions, which gives us differential equations for the concentrations of the minerals. These chemical reactions are very dependent on the temperature in the tank. Because the inflow water may have a different temperature than the tank, we will alsomake a differential equation for the temperature. Using a fourth order Runge-Kutta scheme we can numerically integrate these equations in time. To test the program we use 6 of the most common dissolution reactions in ground water. When using the program we can see that some concentrations change a very insignificant amount and therefore do not contribute to the cloggings. These minerals were Mg 2+ from the dissolution of dolomite and Fe2+ from the dissolution of magnetite. The programworks as desired, but does lack some elements, first and foremost the reactions between acids and bases, such as HCO− 3 and H+.

This thesis describes a study into pairwise particle interactions within a Hele-Shaw geometry, using stop-flow lithography. By exposing a photoreactive mixture to a strong UV-pulse, a hydrogel is formed. The shape of this hydrogel is controlled by masking part of the light beam. This process takes place while the Hele-Shaw channel is placed on the stage of a microscope, which allows these hydrogel particles to be viewed and tracked. Improvements were made to increase the accuracy and precision of the experimental set-up. No- tably, the initially present mismatch of intra-pair particle thickness was greatly reduced by changing the method of particle pair production. By tracking these pairs of particles, information is obtained regarding their motions and velocity relative to one another. Experiments were performed for a selection of particle shapes and compared to numerical simulations of identical geometries. Simulations predicted that attractive and repulsive velocities should be noticed depending on the separation distance and shape of the particles. Qualitatively, the experiments agree to a certain extent with the simulations. It was demonstrated that the pairwise interactions are indeed dependent on their shape. Furthermore, the magnitude of these interactions qualitatively matched with the experimental data. Quantitatively, the experimental data did not agree with the simulations, but strong evidence was presented to indicate that the UV-light hitting the sample was not uniformly distributed. This results in a discrepancy in particle thickness between the pair, which skews the experimental data. Novel insights were gained on the applicability of the current literature model on hydrogel particle propagation. In contrast to the current model, it was experimentally demonstrated that the shape and (in-plane) size of the particle affects its thickness.

Crowd modelling is essential to the understanding of pedestrian logistics and prevention of crowd disasters. Agent-based approaches can realistically predict crowd behaviour. The social force model as proposed by Helbing and Mólnar in 1995[1] is a widely used agent-based approach. This is a physical model for psychological behaviour that relies strongly on its various parameter values. To investigate the underlying thought of the social force model the physical consequences of the effects and parameters are reviewed in this thesis. Next to this, an adjustment onHelbing andMólnar’s model is made by treating agents as particleswith a hard kernel, requiring a walkover- and ghost-prevention functionality. In addition, it is suggested to set the agent interaction magnitude to U0 ®¯ Æ 21 m2/s2. Subsequently, the adjusted model is validated to empirical research done by Seyfried et al.[2] and to simulations done by Helbing andMólnar[1]. For validation a cluster analysis method is developed to give a quantitative measure of the number of lanes.