The environment in which microscopic organisms live in is dominated by viscous forces because of their small length scales. Inertial forces are of little use to them in their propulsion mechanisms. As a consequence of this, an organism such as the scallop which moves through time-reversible deformations of its body would not propel itself in a regime dominated by visocus forces. Hence, microscopic organisms use appendages like cilia and flagella that are not time reversible to move forward. However, inertial effects become important to microscopic organisms at the relevant time and length scales. For example, inertia is used by a microscopic organism such as Paramecium to escape/attack its predator/prey.
The effects of inertia on the model of a spherically ciliated micro-organism are studied numerically using an Immersed Boundary Method (IBM) in the present work. In this model ,the distortions of the envelope that is generated by connecting all the tips of the cilia together, are prescribed. The unsteady Reynolds number which characterizes the influence of unsteady inertia that is generated by the beat of the organism, is varied from 0.025 to 18. The code which uses a Volume Penalization/Volume of Solid IBM to simulate the distorting sphere is validated for several test cases. The mean swimming velocity of the organism that is obtained numerically from the code is in agreement with the analytical model for two cases of the unsteady Reynolds number. The mean swimming velocity is found to decrease at increasing inertia. The flow pattern that is obtained in the near-field as a result of the distorting sphere is significantly different from those obtained with the existing models available in literature.

Transportation of very viscous fluids through pipelines is a real challenge. With the depletion of light oils in reservoirs, it becomes economically favourable to harvest heavy crude oils to contribute to meeting the ever growing energy demand. A suitable candidate for the transportation of these very viscous oil is by means of core-annular flow. Core-annular flow is a flow regime of liquid-liquid two-phase flow, where a low viscous fluid in the annulus (water) is used to lubricate a high viscous fluid in the core (oil). The pressure drop is considerably reduced compared to single phase oil flow at the same oil flow rate.

In this study the influence of the oil viscosity on oil-water core-annular flow through a horizontal pipe is investigated experimentally. The fixed oil flow rate is set at 0.35 l/s at which the watercut is varied between 9% and 25% and the oil kinematic viscosity is altered by heating up the oil in a range from 3000 cSt at 20 °C to 400 cSt at 50 °C. Pressure drop measurements for stable core-annular flow are recorded with an electronic pressure transducer and are scaled with the calculated pressure drop of single phase oil flow.

Results for the scaled pressure drop at room temperature are compared to results by Ingen Housz et al. It is concluded that for increasing oil-water viscosity ratio, the scaled pressure drop decreases. At the highest considered viscosity ratio, the scaled pressure drop is almost independent of the watercut. Two models to predict the pressure drop (by Brauner and by Bannwart) are evaluated and deviations between the models and measurements are discussed. Visualisation by means of high-speed camera is applied, where a mirror is placed on top of the visualisation section to capture the front and top view simultaneously. For decreasing oil viscosity, the oil-water interface shows a more irregular wave pattern with shorter wave lengths.

Core-annular flow is an efficient flow regime for the transportation of viscous oils. The viscous oil in the core is surrounded and lubricated with an annulus of water. Water has a low viscosity and therefore reduces the pressure drop. Numerical simulations are performed for horizontal core-annular flow by using the Volume of fluid (VOF) method to solve the Reynolds-averaged Navier-Stokes equations (RANS) in OpenFOAM. Periodic boundary conditions are used for a small pipe section. With periodic boundary conditions the maximum wavelength at the oil-water interface is imposed together with the oil and water holdup fractions.

Numerical results are compared with recent experimental data. Oil viscosities between 3338 cSt at 20°C and 383 cSt at 50°C are solved with a fixed total flow rate. The 20°C simulation converged to the desired water cut of 20%, similar to the experiment. At this 20% water cut a comparable pressure
gradient is found with the experiment. At higher temperatures (i.e. lower viscosities) deviations from the desired water cut of 20% are obtained. The different water cut values lead to differences between the numerical and experimental pressure gradients.

Additional simulations are carried out for the oil viscosity of 718 cSt at 40°C. Instead of a fixed total flow rate these simulations are solved with a fixed pressure gradient. This solving method is found to be considerable faster. Different holdup fractions and pressure gradients are imposed which resulted in different water cut and flow rate values. Numerical results are interpolated for the experimental water cut values of 9%, 12% and 15% at similar flow rates. Differences of 98%, 24% and 37% are found for the water cut of 9%, 12% and 15% respectively. An interpolation is not possible for the experimental water cut of 20% as this experiment is outside the covered solution region of the numerical results. This difference is caused due to an incorrectly used domain length.

The study is finished with holdup estimations of the experiments. Flow visualizations from a high speed camera are used which are made during the experiments. Oil holdup fractions of 0.749 are found for a water cut of 20%. This holdup fraction corresponds exactly with the imposed holdup fraction for the different viscosity simulations which are solves with the fixed total flow rate. Only the 3338 cSt at 20°C converged, however, to the water cut of 20%.