| dc.description.abstract | In this thesis, we have developed a computational method for two-phase electrohydrodynamics (EHD) problem. The method is based on a three dimensional level-set method and the leaky-dielectric EHD model. Level-set method is used for modelling the interface of the two-phase flow system. The electrostatic phenomenon is dealt with the leaky dielectric-leaky dielectric fluid system. In leaky dielectric-leaky dielectric fluid system, both the fluids have small but finite electric conductivity. Upon application of the external electric field, all charges from both fluids accumulate at the interface leaving the bulk free of any charge. At first, we have validated our developed model against existing results from literature. After validation, we have implemented the developed code in a practical application of droplet sorting using non-uniform electric field known as dielectrophoresis (DEP). At present there is no existing computational method on DEP assisted droplet sorting which leads our present analysis a complete novel contribution in this field. For validation, two classical flow cases are tested: (a) a droplet subjected to a uniform electric field; (b) a droplet subjected to both uniform electric field and shear flow. For both of the cases, results obtained from present computational method show good agreement with the existing results from literature. For droplet subjected to a uniform electric field case, depending on the conductivity (K) and permittivity(Q) ratio of the two fluids, we have obtained three types of droplet deformation namely prolate A, (PRA : KQ > 1), prolate B(PRB : KQ < 1), and oblate (OB : KQ < 1) drop. The deformation parameter obtained from the present simulation are quantitatively validated against the existing analytical, numerical and experimental results. For a droplet subjected to both uniform electric field and shear flow, we have analysed the effect of hydrodynamic capillary number, Ca (ratio of viscous force to and surface tension force) and electric capillary number CaE (ratio of electric stress to and surface tension force) on the droplet deformation and breakup. A phase diagram is also established as a function of Ca and CaE which depicts that the combined effect of electric stress and shear flow promotes the breakup of the droplet even at smaller Ca which is not possible if there is only shear flow. Results obtained from this case also show good agreement with the numerical results of existing literature. In the second part, we computationally study the motion of an initially uncharged spherical droplet flowing through a straight rectangular channel with an orthogonal side branch, using a three-dimensional level set method. The spatially non-uniform electric field is created by placing an electrode at the bottom of the channel. We mainly focus on the sorting of the droplet without and with electric field effect as a function of different parameters of the problem namely branch flow ratio, q (ratio of the flow rate in the side branch to the flow rate in the main channel), electric capillary number CaE (ratio of electric stress to surface tension), different positions of the electrode, low and high flow Reynolds number Re (ratio of inertia force to and viscous force) and finally different size ratio, λ (ratio of droplet radius to half cross sectional length of the channel). In this research, we mainly investigate the path selection of the droplet when subjected to the above mentioned parameters. Depending on the intensity of the physical parameters, the droplet can flow into either the downstream main channel or it can sort into the orthogonal side branch. The sorting of a droplet is characterized by the critical branch ratio, qc above which the droplet enters the side branch. Without electric field, it is obtained that at low Re, the droplet favours the branch which receives higher flow rate. However, inertia has a significant effect on the path selection of droplet. When Re is increased to 20, it has been found that the droplet enters the main channel even when it receives much less flow than the side branch. For spatially non-uniform electric field, we have considered two different intensities of electric field through the value of electric capillary number CaE = 0.4 and 0.9. We obtain that higher the intensity of electric field, larger the electric force which can sort the droplet at a lower value of qc. We also analyse two electrode positions namely electrode 1 and 2. At electrode 1 position, the electrode is placed closer to the initial position of the droplet compared to the electrode 2 position. It has obtained that with both electrode positions a significant reduction of qc is achieved. However at electrode 1 position, a greater reduction of qc is obtained compare to electrode 2 position both at low and high inertia regime. In addition to it, we investigate different size ratios λ = 0.2, 0.3 and 0.4, on the path selection of the droplet when electrode is placed at position 1 with CaE = 0.9 at high inertia regime. It is obtained that larger the value of size ratio (λ), higher the value of dielectrophoresis motion (motion of the droplet due to non-uniform electric field) which promotes the droplet sorting at side branch even at lower branch flow ratio with high inertia effect. Finally, from the present investigation we conclude that electrode at position 1 with CaE = 0.9 and λ = 0.4, the critical branch flow ratio is the lowest qc which is 0.08. The results and conclusions from the present thesis facilitate the understanding of the fundamental principles and mechanisms of electrohydrodynamics (EHD) based droplet deformation, breakup and sorting of the droplet using dielectrophoresis in microfluidic channel. Therefore, present results can have potential usefulness towards the design and development of droplet-based microfluidic devices. | en_US |
