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Bioelectrochemical cells utilize bacteria in order to extract electricity from organic compounds, for example found in wastewater streams. This process occurs within a thin layer of bacterial cells, the biofilm, on either the anode or cathode. Using a physics based modelling approach, four main processes in the (anode) biofilm are considered; ionic transport coupled to acid-base reactions, biochemical conversion of acetate species, electron transfer to a network of conductive pili, and charge transport through the pili towards the electrode. Results obtained by De Lichtervelde et al. [Physical Review applied, vol. 12, no. 1, p. 014 018, 2019] are replicated, showing a reproducibility of the model. These results indicate that an accumulation of protons within the biofilm limits the current that can be extracted from the bioelectrochemical cell. Based on the electric potential profile within the biofilm, the question arises if the local electroneutrality condition can be used within these kinds of systems. To investigate this, a first attempt in adding the Poisson equation to the system is made. Based on length-scale considerations, the results obtained from using the local electroneutrality condition seem reliable, but the potential profile should be interpreted with caution.

In this thesis fluid fluxes and electric charge fluxes as a result of a pressure gradient, electric field or salt concentration gradient, through a nanopore with a charged surface, are considered. It is found that the fluxes react linearly to the considered driving forces. Every driving force induces not only its conjugate flux but also all other Fluxes. By solving the Poisson-Nernst-Planck-Stokes equations numerically, fluxes as a result of salt concentration gradient driven flow through a chain of nanopores, a membrane, can be simulated. From these simulations an optimal geometry is found to maximixe the generated power per unit volume membrane.

We construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory, we are not only able to describe the isotropic-nematic phase transition as function of density, including the well-known density jump, but also the isotropic-nematic planar interface. The resulting theory is applied in calculations of the isotropic core size in a radial hedgehog defect, the density dependence of linear defects of hard rods in square confinement, and the formation of a nematic droplet in an isotropic background.

At any place where a river flows into the sea, fresh and saline water are mixed. This salinity-gradient energy or ``blue energy" can be harvested, e.g. using capacitive mixing. The reverse process is also possible: water desalination using capacitive demixing in a three-step cycle. In this thesis, the aim is to find the optimal desalination cycle, such that the required work per liter desalinated water is minimal. In order to find the optimal cycle, the parameter space of two variables is explored: the temperature, and the ratio between the engine volume and the water volume that is made fresh during one cycle. Numerical solutions to the lattice-gas Poisson-Boltzmann equation for parallel-plate capacitors show that desalination processes are the most efficient at low temperatures. Calculations regarding the volume ratio indicate that desalination processes are the most efficient for the case when the volume of secured fresh water per cycle is large compared to the engine volume.

In this thesis ion distributions are predicted by means of Poisson-Boltzmann theory. In its simplest form the Poisson-Boltzmann equation, which strongly builds upon Gouy-Chapman's treatment of a single planar charged surface in contact with a half space of electrolyte, describes the interaction of point-like ions in a structureless continuum solvent via their self-consistent mean field. A recent experimental study of ion concentrations near an electrified oil-water interface provided the inspiration for an extension of this classical analysis. The ionic self-energy differences in oil and water, as well as the presence of two planar walls (rather than one) are incorporated to describe the ion distributions near an oil-water interface within an electrolytic cell.

An enormous dissipation of the order of 2 kJ/L takes place during the natural mixing process of fresh river water entering the salty sea. "Capacitive mixing" is a promising technique to efficiently harvest this energy in an environmentally clean and sustainable fashion. This method has its roots in the ability to store a very large amount of electric charge inside supercapacitor or battery electrodes dipped in a saline solution. Three different schemes have been studied so far, namely, Capacitive Double Layer Expansion (CDLE), Capacitive Donnan Potential (CDP) and Mixing Entropy Battery (MEB), respectively based on the variation upon salinity change of the electric double layer capacity, on the Donnan membrane potential, and on the electrochemical energy of intercalated ions.

For hard anisotropic particles the formation of a wide variety of fascinating crystal and liquid-crystal phases is accomplished by entropy alone. A better understanding of these entropy-driven phase transitions will shed light on the self-assembly of nanoparticles, however, there are still many open questions in this regard. In this work, we use Monte Carlo simulations and free-energy calculations to determine the phase diagram of colloidal hard superballs, of which the shape interpolates between cubes and octahedra via spheres. We discover not only a stable face-centered cubic (fcc) plastic crystal phase for near-spherical particles, but also a stable body-centered cubic (bcc) plastic crystal close to the octahedron shape. Moreover, coexistence of these two plastic crystals is observed with a substantial density gap. The plastic fcc and bcc crystals are, however, both unstable in the cube and octahedron limit, suggesting that the local curvature, i.e. rounded corners and curved faces, of superballs plays an important role in stabilizing the rotator phases. In addition, we observe a two-step melting phenomenon for hard octahedra, in which the Minkowski crystal melts into a metastable bcc plastic crystal before melting into the fluid phase.

Phase diagrams of binary mixtures of oppositely charged colloids are calculated theoretically. The proposed mean-field-like formalism interpolates between the limits of a hard-sphere system at high temperatures and the colloidal crystals which minimize Madelung-like energy sums at low temperatures. Comparison with computer simulations of an equimolar mixture of oppositely charged, equally sized spheres indicate semiquantitative accuracy of the proposed formalism. We calculate global phase diagrams of binary mixtures of equally sized spheres with opposite charges and equal charge magnitude in terms of temperature, pressure, and composition. The influence of the screening of the Coulomb interaction upon the topology of the phase diagram is discussed. Insight into the topology of the global phase diagram as a function of the system parameters leads to predictions on the preparation conditions for specific binary colloidal crystals.

In the wake of previous studies on the rattling-and-jumping diffusion in smectic liquid crystal phases of colloidal rods, we analyze here for the first time the heterogeneous dynamics in columnar phases. More specifically, we perform computer simulations to investigate the relaxation dynamics of a binary mixture of perfectly aligned hard spherocylinders. We detect that the columnar arrangement of the system produces free-energy barriers that the particles should overcome to jump from one column to another, thus determining a hopping-type diffusion. This phenomenon accounts for the non-Gaussian intercolumn diffusion and shows a two-step structural relaxation that is remarkably analogous to that of out-of-equilibrium glass-forming systems and gels. Surprisingly enough, slight deviations from the behavior of simple liquids due to transient cages is also observed in the direction perpendicular to this plane, where the system is usually referred to as liquidlike.