The present thesis aims to develop a Lab-on-Chip (LOC) platform technology for mixing, separation, and trapping of biological samples, in particular for handling biological and non-biological particles with application in three-dimensional tissue printing and point of care diagnostics. Numerical models for the different manipulation tasks were first established. Physical parameters such as magnetic flux density, pressure, velocity of the fluids, particle trajectory, and species concentration were numerically simulated. The numerical model was then used to optimise mixing, separation, and trapping of biological particles such as cells and exosomes. Hydrodynamic trapping of three-dimensional (3D) spheroids was demonstrated as a passive separation method. The developed LOC device facilitates trapping, culturing and fusion of cell spheroids in a single system. The successful test of the device indicates its potential therapeutic application in the repair of nerve injuries. Furthermore, active manipulation was employed to initiate mixing and separation of non-magnetic particles using negative magnetophoresis. The proposed mixing platform offers an optimised and low-cost solution by separating the permanent magnets from the LOC device. Separation of nonmagnetic fluorescent particles with a subtle size difference was demonstrated. The problem of clogging the channel by magnetic nanoparticles was solved by introducing multiple ferrofluid streams with different concentrations. Finally, positive magnetophoresis was utilised to implement on-chip mixing and subsequent separation of a biological sample for cancer detection. The device with integrated sample preparation promises applications in Point-of-Care (POC) diagnostics of early stage cancer.