Inkjet printing involves several key challenges. An important aspect is the flow dynamics after deposition of an ink droplet onto a substrate. The drop will evaporate and -- if the substrate is porous -- absorb at the same time. Typically, this process also involves additional components like surfactants. Surfactants are molecules that adsorb onto interfaces, thereby reducing the local surface tension, which has significant ramifications for the droplet dynamics. The reduced interfacial tension can result in rich behavior, including circulatory flow patterns and accelerated absorption dynamics. It is therefore of no surprise that there are still many open questions regarding the mechanisms of surfactants in sessile droplets. In this thesis an attempt is made to answer some of these questions in a satisfactory way.In order to gain insight into the dynamics of surfactant-laden droplets, a numerical model is employed. This model is based on lubrication theory, meaning that the assumption is made that the contact radius of the droplet has a significantly larger magnitude that the height. By making this assumption it becomes possible to describe the droplet evolution only in terms of a height profile, making lubrication theory an efficient and transparent modeling technique. With this model as a basis, several extensions are introduced of which the surfactant transport is the most prominent one. This transport is governed by several convection-diffusion-adsorption equations both at the interfaces and in the bulk of the fluid. Furthermore, absorption into the porous medium is modeled with Darcy's law and the evaporation field is calculated using an analytical solution.First, the contact line dynamics of an evaporating droplet with insoluble surfactants are examined using two different methods: a precursor film model and a slip model. For pure droplets these models are shown to perform comparably with respect to literature data, but when surfactants are involved the precursor film model results in several problems, because it does not inherently distinguish between the droplet and the film. Therefore, surfactants can freely flow in and out of the precursor film, which is an issue that requires to be solved before this model can be used in the current context. The slip model, on the other hand, reveals that even if there is no explicit pinning force present, surfactants can still keep the contact line fixed. This is caused by the reduction in space on the interface during evaporation, which increases the surfactant concentration and decreases the surface tension accordingly. The result is a lower equilibrium contact angle, which slows down the contact line retraction as if actually pinning it.Furthermore, the various regimes of the fluid flow in evaporating droplets with soluble surfactants are mapped. It is shown that with the inclusion of surfactants typically one out of two flow patterns exists: a circulatory flow, where there is the combination of an outward capillary flow in the bulk of the droplet and an inward Marangoni flow close to the interface (called the `Marangoni regime'), and a purely outward flow, where there is only a capillary flow towards the contact line, while the flow at the interface nearly halts due to Marangoni effects (called the `coffee-ring regime'). Surfactant properties that are found to typically promote the Marangoni regime over the coffee ring regime are fast sorption kinetics and high solubility, while for the droplet conditions fast evaporation is a promoting factor. Also, the absorption of droplets in porous media is modeled and the effects of surfactants on this process are analyzed. It is found that for pure droplets with both pinned and moving contact lines the penetration depth, being the deepest point where fluid has absorbed, evolves in a similar manner. However, for a moving contact line case the absorption process is much slower than for a pinned case, because the contact area shrinks over time. This also results in the wetted region having a more pointed shape after absorption in the moving contact line case. It is shown that surfactants can accelerate the absorption process, but only if the adsorption kinetics are not too fast compared to the absorption time scale. Otherwise, all surfactant adsorbs onto the pore walls before reaching the wetting front.Lastly, a start is made with developing a model that describes particle transport during evaporation, both for small and large concentrations. For small concentrations, the colloidal dynamics can be described by a `tracer particle model', where the particles are considered to be massless and passive. For the tracer particle model it is shown that the lubrication model does not describe the velocity field in the contact line region accurately. If a circulatory flow is present, particles still accumulate at the contact line as if there is only a capillary flow. Possible solutions to this issue lie in the introduction of correction terms that are otherwise neglected in lubrication theory or to use an altogether different model that fully incorporates the Navier-Stokes equation for viscous flows. At higher concentrations, the particle dynamics can be described by a `two-phase model', where the particles are considered as a distinct phase that affects the fluid dynamics. It is found that any two-phase particle model for evaporating droplets requires to take into account the maximum packing density of particles, since this concentration is already reached in the initial stages of the drying process. By introducing several ad-hoc corrections when the maximum packing density is reached, it is shown that reasonable results can be obtained. However, in order to make the model viable it also needs to take into account the underlying physics, which can possibly be achieved by modeling the transition from a Stokes regime flow to a Darcy regime flow at high particle fractions
