Numerical Simulation of Digital Microfluidics Based on Electro-Dynamic Model

Numerical Simulation of Digital Microfluidics Based on Electro-Dynamic Model

Liguo Chen, Mingxiang Ling, Deli Liu
Copyright: © 2012 |Pages: 10
DOI: 10.4018/ijimr.2012070102
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Aiming at the doubt and divarication about the internal mechanism of electrowetting on dielectric (EWOD) in digital microfluidics, the authors attempted to explain the internal mechanism of EWOD through electro-dynamic-based numerical simulation model. First, the boundary conditions for the governing equation were found. Then the influence of mesh number on simulation results was analyzed and feasibility of the simulation model was verified by comparing numerical results with theoretical ratiocination. Finally, they compared the electro-dynamic actuation force acting on the surface of droplet on three digital microfluidic structures, which have the same three-phase contact line but different area of contact domain. Analytical results showed that electro-dynamic force generated solely by the accumulation of induced charges in contact domain was three times larger than that generated by three-phase contact line. Induced charges accumulated on both three-phase contact line and contact area of droplet gave the contribution to EWOD, but contact area played a major role in the change of contact angle of droplet.
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Since A. Manz proposed the conception of Micro Total Analytical System (μ-TAS) for the first time in 1989 (Manz, Graber, & Widmer, 1990), digital microfluidics based on EWOD, in which droplets are manipulated and controlled on an array of electrodes, has been greatly used inchemistry, biology and medicine, and has tremendously and revolutionaries promoted the development of all these subjects (Berge & Peseux, 2000; Heikenfeld & Steckl, 2005; Lidija & Daniel, 2009). Thanks to its high-throughput, high-sensitivity, extremely low consumption and faster analytical times, the use of droplets in digital microfluidics as chemical reactors for polymerase chain reaction (PCR) (Chang et al., 2006), carries of cells or DNA for cell manipulation or DNA enrichment and ligation (Irena, Aaron, & Wheeler, 2010) and so on, has drawn extensive attention in almost all countries.

EWOD can be defined as the changes of contact angle of liquid droplets at three-phase contact line through an external applied voltage. The mathematical relation between contact angle and the applied voltage satisfies the Young-Lippmann equation as follows (Choet al., 2003; Lee et al., 2002; Moon et al., 2002; Mugele & Baret, 2005; Vallet & Berge, 1999):

(1) here, θ is contact angle under applied voltage V, θo is initial contact angle, εo is the electric permittivity of vacuum, γl-g is the interfacial tension between droplet and the surrounding medium (air or silicone oil), d and εr is the thickness and relative permittivity of dielectric layer, respectively.

Although the manipulation and control of liquid droplets over hundreds of cycles by applying a moderate voltage (dielectric layer tends to breakdown and contact angle is apt to saturate under very high voltage) has been successfully implemented in either single-plate or two-plate digital microfluidicsby different investigators (Sung & Hyejin, 2003; Vijay & Richard, 2004), there are two attitudes toward the internal mechanism of EWOD. Berge et al suggested that capacitance effect between liquid-dielectric interfaces induced the change of contact angle. That was, the accumulation of induced charges due to the extensive applied voltage changed the free-energy between liquid-dielectric interface, and then the interfacial tension was also changed in order to maintain the minimum status of interfacial free-energy (Quilliet & Berge, 2001; Shawn & Benjamin, 2006). The above interpretation was doubted by some investigators, considering that the density of induced charges of the electrical double layer in the liquid droplet was too significant to drive such a large change of contact angle (Peykov & Quinn, 2000). In contrast with the minimum interfacial free-energy, Dilov et al. proposed (Berthier & Peponnet, 2007; Digilov, 2000) that the reduction of contact angle was due to electrostatic force originating from the accumulation of induced charges at the three-phase contact line of droplet. And it is widely believed that the tree-phase contact line is the reason for larger electro-dynamic force generation.

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