TECHNICAL PAPER A liquid-state high sensitive accelerometer based on a micro-scale liquid marble Mina Ghanbari 1 • Ghader Rezazadeh 2 Received: 20 May 2019 / Accepted: 25 June 2019 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In this paper, the dynamic behavior of a high sensitive liquid marble based accelerometer in the presence of the external acceleration field is investigated. The presented scheme for this study consists of a liquid marble placed on a curved surface bounded with another fixed surface above it. In order facilitate the marble displacement and therefore increase the accelerometer sensitivity, the marble is manipulated electrostatically by applying a DC voltage to the fixed top and bottom curved surfaces. The produced electrostatic force deforms the marble by opposing its weight, therefore causes the marble to get spherical form approximately. In the following, the nonlinear equation governing the motion of the liquid marble in the existence of the external acceleration is derived. To study the marble stationary behavior, the equation has been solved by utilizing the weighted residual method. It has been shown that by decreasing the contact zone area of the marble, the minimum external acceleration required to start the rolling motion of the liquid marble decreases. Investigating the frequency response of the accelerometer has also shown that for the external acceleration value lower than 0.04 g, the accelerometer shows linear stationary behavior. 1 Introduction An electromechanical sensor that measures acceleration forces is called accelerometer. The forces may be dynamic caused by vibration or movement of the accelerometer or static like constant gravity force. An accelerometer behaves as a damped mass on a spring, conceptually. When the accelerometer is exposed to an acceleration field, the mass displaces and the acceleration is given by measure- ment of the mass displacement. Many types of classical accelerometers were developed and reported in the past researches. As most of the classical sensors were designed based on piezoelectric crystals, they couldn’t be applicable in various fields due to their enormous size. Recently, a new generation of micro-devices as micro-electro-me- chanical systems (MEMS) have become extremely attrac- tive among scientists and researchers. They have several benefits as small size, low production cost and low consumption of energy. Micro-pumps (Saif et al. 1999), micro-mirrors (Rezazadeh et al. 2007; Afrang et al. 2019) micro-accelerometers (Tran et al. 2014), microfluidics (Pawinanto et al. 2019) and micro-sensors (Rezazadeh et al. 2010) are examples of micro-scale devices. Among them, micro-accelerometers are one of the simple and most applicable micro-electro-mechanical systems. The MEMS accelerometer operation is based on the movement of a small solid proof mass scratched into the integrated circuit of silicone surface and suspended by small size beams. These solid-state sensors can be used in various fields of engineering and sciences. For example, in aerospace applications, accelerometers can be used along with gyro- scopes for flight control and navigation guidance. In civil engineering, in cable-stage bridges, they can be utilized for identification of tension and for monitoring of composite structures. They can also be implemented in medical devices like artificial body parts and bionic limbs. Although solid-state accelerometers are effective and provide higher sensitivity compared to liquid-state sensors, the suspended proof mass incorporation causes the assembly, manufacturing, and packaging of the sensors to be more complex. To overcome these complexities researchers have begun to study on liquid-state motion sensors. Zeng and Zhao in one of their worthy studies & Mina Ghanbari m.ghanbari@urmia.ac.ir 1 Mechanical Engineering Department, Engineering Faculty of Khoy, Urmia University, Urmia, Iran 2 Mechanical Engineering Department, Faculty of Engineering, Urmia University, Urmia, Iran 123 Microsystem Technologies https://doi.org/10.1007/s00542-019-04528-7