Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.


Mechanical Engineering

Committee Chair

Lian, Yongsheng

Committee Co-Chair (if applicable)

Brehob, Ellen G.

Committee Member

Brehob, Ellen G.

Committee Member

Harnett, Cindy

Committee Member

Sharp, Michael K.

Committee Member

Williams, Stuart




Particle information such as particle size and amount is significant to many fields such as chemical engineering, biological research, medical analysis, and environment detection. Microfluidic Coulter counter is suitable for this task because it can get fast and accurate analysis. However, the fundamental principle and several design strategies details are still needed to be analyzed and modeled in order to improve its performance. This dissertation focused on several challenges from the numerical simulation aspects. First one is the analysis for the hydrodynamic focusing in microfluidic Coulter Counter. In recent years, many microfluidic Coulter Counter designs have utilized a technique termed “hydrodynamic focusing” to control the particle’s trajectory. Hydrodynamic focusing uses two sheath flows (low concentration) to squeeze the sample flow (high concentration) so it can concentrate the ion distribution on the region where the designer wants. There are large concentration difference between the sample stream and sheath stream. However, few published papers mentioned the ion concentration distribution under the impacts of hydrodynamic focusing. This is difficult to deal withbecause there are conductivity differences at the interface of the sheath/sample streams and the interface of the sample stream/particle. A very fine grid mesh is needed to capture the ion concentration distribution. Meanwhile the simulation which runs at low Reynolds number requires a rigorously smaller than usual time interval to satisfy the stability condition. Another challenge which this dissertation faced is the particle motion. The key point for particle motion simulation is the grid regeneration since the grid needs to be adaptive with the particle movement. So far many simulation solvers choose to regenerate the whole grid domain after each time step. This strategy takes a huge amount of time. The third challenge is the simulation for the electrical potential by considering the significant conductivity difference between the particle and medium. The numerical simulation process gets unstable when the conductivity distribution is not uniform and becomes worse if there is a sharp conductivity variation in the distribution. A new mathematical difference method is needed to model the potential distribution. In order to overcome these challenges, this dissertation used an “overlap mapping” grid generation method to capture the ion concentration distribution along the interfaces of sheath/sample stream and sample stream/particle. The grid regeneration was only needed for the moving object in order to save computing time. A new center difference method was applied on the electrical potential equation to solve its stability problem. The numerical simulation studied the impacts of hydrodynamic focusing with considering the ion convection-diffusion phenomenon. We found that the fluid viscosity does not play a significant role in the concentration distribution. The max concentration relative error is no more than 2.5% on the peak of the selected cross section. Also, the diffusion phenomenon can dilute the ion concentration focusing ability by hydrodynamic focusing while larger sample/sheath stream flow rates ratio can improve the concentration value. The hydrodynamic focusing can decrease the vertical gap between the particles while increasing their horizontal gap. After that the current signal variation were simulated and it showed that the diffusion phenomenon can decrease the signal sensitivity. For the particle we choose to simulate, the current sensitivity decreases 29% in 2D simulation. Fluid viscosity does not play a significant role in the current signal variation if we choose the Reynolds number between one and ten (The max current variation is 3.6% for the 3d simulation). The electrodes length/position, particle size and particle position also affected the current signal. The numerical simulation approaches and results from this dissertation updated the understanding of hydrodynamic focusing and Coulter Counter principle. Also this dissertation showed the feasibility to study the Coulter counter principle numerically by considering the diffusion phenomenon and particle motion.