• direct numerical simulations
• engulfment regime
• global stability analysis
• microfluidics
• t-mixer
• vortex regime

Efficient mixing between two or more fluids in small volumes is a key target in many processes. Among the most common micro-devices, T-shaped micro-mixers are widely used. For this reason T-mixers have been studied in the literature and their working flow regimes have been identified and characterized. In particular the transition between the vortex regime and the engulfment regime received large attention because the onset of the engulfment regime promotes significantly the mixing process. In most of the available theoretical and numerical studies it is assumed that the same fluid at the same thermodynamic conditions is entering the two inlet conduits of the mixer. Conversely, the practical use of micro-devices often involves the mixing of two different fluids or of the same fluid at different conditions.
The goal of this thesis is the study of the vortex and engulfment regime in a T-mixer when water at two different temperatures is entering the mixer. In particular we focus on the effect of the temperature onset of the engulfment regime. While density variations are weak and can be neglected, variations in viscosity can be significant for water, depending on the temperature difference of the two streams entering the mixer. Therefore, the considered flow configuration can be used to study the effects of viscosity variations on the vortex and the engulfment regimes. A specific T-mixer geometry is considered here which has been previously characterized in details by direct numerical simulation (DNS) and stability analysis when only one working fluid is employed. Here we use the same tools, i.e. DNS and stability analysis, to investigate the case in which water at two different temperatures is entering the mixer and we consider temperature jumps up to 40°C.
In first place the case of a plane T-mixer it has been studied: we characterized the imperfect pitchfork bifurcation that occurs when water at different temperatures is considered and we validated the linear stability code. Then we describe the effect of the temperature on the flow regime for the 3D case studied by means of DNS. The analysis shows the effect of the temperature jump on the vortical structures and on the fluid motion both for the vortex and the engulfment regime and describes the transition process that leads from the first to the second flow configuration. Moreover the degree of mixing for different values of the temperature jump and of the Reynolds number has been investigated. Finally we compared the results obtained with DNS and global stability analysis both for the values of the critical Reynolds and for the perturbation field. The result are in agreement and show that higher values of the temperature jump promote the onset of the engulfment regime.