European Journal of Mechanics / B Fluids 76 (2019) 292–302 Contents lists available at ScienceDirect European Journal of Mechanics / B Fluids journal homepage: www.elsevier.com/locate/ejmflu Revealing electrical stresses acting on the surface of protoplast cells under electric field Kia Dastani a,b , Mahdi Moghimi Zand a,c,d,∗ , Amin Hadi a , Changyong Cao c,d,e,∗∗ a Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, 14399-55961, Iran b Department of Mechanical Engineering, Sharif University of Technology, 11155-9567, Tehran, Iran c Laboratory of Soft Machines and Electronics, School of Packaging, Michigan State University, East Lansing, MI 48824, USA d Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA e Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA article info Article history: Received 14 August 2018 Received in revised form 3 February 2019 Accepted 25 February 2019 Available online 12 March 2019 Keywords: Cell engineering Dielectrophoresis Microfluidics Immersed interface method (IIM) BioMEMS abstract When cells exposed to an electric field, localized changes in the distribution of the electric field will be induced and these changes in turn lead to electrical stresses on cell surface. The electrical stresses play a key role in the cell membrane structural changes which leads to important phenomena like hydrophilic pores formation on the cell membrane resulting in the cell permeability. In this work, protoplast cell interaction with direct current (DC) electric field is investigated. The electrical stresses acted on the cell membrane in the presence of electric field are investigated numerically by a modified finite difference method, fast Immersed Interface Method (IIM). Exact solution of dielectrophoresis (DEP) force applied on a cell under a non-uniform electric field is obtained to verify numerical solution obtained by the fast IIM. The numerical results reveal that both mismatched permittivity between cell and insulating suspension fluid and the applied voltage are essential for generating and tuning the total stresses exerted on cell surface. This paper can help to analytically study the electroporation phenomenon which its exact mechanism is still unclear. © 2019 Elsevier Masson SAS. All rights reserved. 1. Introduction Significant progresses have been made in mammalian cell engineering over past years for the modification of cellular function such as gene expression [1–8], protein processing [9–12], secretion [13–15], glycosylation [16,17] and proliferation [18–21]. One of the most important aims of cell engineering is to improve the cellular properties of cells for applications in cell therapies and tissue engineering. Electroporation is one of the promising approaches to transfer macromolecule into cell. It allows one to introduce exogenous molecules into cells and simultaneously to extract endogenous molecules from inside of the cells [22]. The formation of hydrophilic pores on the surface of cell membrane makes the cell permeable for achieving this process. The pores are formed by the tension stress exerted on the cell membrane, either mechanically (pipet aspiration) or electrically (electroporation). ∗ Corresponding author at: Small Medical Devices, BioMEMS & LoC Lab, Department of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, 14399-55961, Iran. ∗∗ Corresponding author at: Laboratory of Soft Machines and Electronics, School of Packaging, Michigan State University, East Lansing, MI 48824, USA. E-mail addresses: mahdimoghimi@ut.ac.ir (M. Moghimi Zand), ccao@msu.edu (C. Cao). Up to now, the formation mechanism of the pores caused by electrocompressive stresses has not yet been understood well. It is generally believed that the transmembrane potential reaches a critical value to make cell to rupture. The rupture or irreversible membrane breakdown happens when the pore radius becomes more than a critical value [23]. Membrane rupture mechanism under electric field is also unclear like membrane permeabiliza- tion. Electrical stresses should have an important role in both phenomena. Different theoretical models have been proposed to explain this electroporation phenomenon. The transient aqueous model is one of the most accepted models. It assumed that when cell is exposed to an electric field, the induced transmembrane po- tential (TMP) provides free energy for phospholipids orientation in the cell membrane, leading to the formation of hydrophilic pores [24–26]. In a previous study, the effect of electric field on cell membrane permeability has been investigated indirectly by measuring the conductivity changes caused by applying electrical pulses and observing molecular transport into cells [27]. TMP depends on cell radius, the electric field intensity, the angle between membrane points and direction of the electric field. It can be calculated by the Schwan’s equation [28]. It has been observed that molecule transfection happens more in the part https://doi.org/10.1016/j.euromechflu.2019.02.010 0997-7546/© 2019 Elsevier Masson SAS. All rights reserved.