1 3 Microsyst Technol (2016) 22:2223–2232 DOI 10.1007/s00542-015-2624-2 TECHNICAL PAPER A new method for the interaction between multiple DEP particles: iterative dipole moment method Le Liu 1 · Chuanchuan Xie 1 · Bo Chen 1 · Ng Chiu‑On 2 · Jiankang Wu 3 Received: 5 April 2015 / Accepted: 7 July 2015 / Published online: 28 July 2015 © Springer-Verlag Berlin Heidelberg 2015 1 Introduction Dielectrophoresis (DEP) is one of the most popular tech- niques for bio-particle manipulation in microfluidic systems. Since first defined by Pohl (1978), DEP has attracted a lot of attention over the past decades. Because of its simplicity, DEP is widely used for cell separation, trapping (Gascoyne et al. 2009; Hughes 2002) and bio-structure assembling (Castillo et al. 2008), as well as nanostructure (e.g., carbon nano-tube) deposition (Duchamp et al. 2010). Ignoring par- ticle interaction, the dielectrophoretic forces and motions of particles can be calculated by the method of equivalent dipole moment (EDM) (Morgan et al. 1999; Çetin and Li 2011). However, the EDM is accurate only in the dilute limit of the particle density. Particle interactions, which determine the particle kinetics, may become significant when parti- cles get close to another. The Maxwell stress tensor (MST) method has been considered as the most rigorous method to determine the dielectrophoretic forces in general (Al- Jarro et al. 2007; Rosales and Lim 2005; Wang et al. 1997). Based on the MST, Ai and Qian (2010) investigated hydro- dynamic particle–particle interactions in a uniform electrical field using a transient multiphysics model, where the fluid flow, electric field and particle motion were simultaneously solved using an arbitrary Lagrangian–Eulerian (ALE) algo- rithm. Kang and Maniyeri (Kang and Maniyeri 2012) per- formed a direct numerical simulation of two-dimensional DEP interaction of multiple particles suspended in a viscous fluid subjected to a uniform electric field. House et al. (2012) numerically studied the DEP interaction between two prolate spheroid particles in an unbounded fluid using the boundary element method (BEM). Hossana et al. (2013) presented a numerical simulation of two-dimensional DC dielectro- phoretic particle interactions using an interface-immersed method. Kurgan (2011, 2012) made a comparison between Abstract Dielectrophoresis for bio-particle manipula- tion has been drawing much attention in recent years. The equivalent dipole moment has been widely used to calcu- late dielectrophoretic forces on a particle, but this method falls short to describe the interaction between neighbor- ing particles. The Maxwell stress tensor method (MST) is theoretically rigorous for particle interaction, but it will cost huge computing resource. In this paper, an iterative dipole moment method (IDM) is presented to investigate the interaction between multiple dielectrophoretic parti- cles in a two-dimensional electric field. Without any cum- bersome numerical computation, the inter-particle forces and the particle trajectories calculated by the IDM method are found to be in good agreement with those by the MST method for some published results. Furthermore, it is found that the final stable particle chain patterns strongly depend on the initial configuration of the particle distribution. An arbitrary small disturbance to the particle locations may lead to dramatically different motion trajectories and final particle chains. Supported by National Science Foundation of China, No. 11172111. * Bo Chen chbo76@hust.edu.cn 1 School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China 2 Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China 3 Wenhua College, Wuhan 430074, China