Fatih DIKMEN, Ibrahim EFE, Yury TUCHKIN

On an electrostatic micropump with a rigorous mathematical model

The novel electrostatic micropump model for applications such as in biomedical drug delivery is presented. The geometrical arrangement of the coupling rigid electrodes lets us exploit our mathematically rigorous boundary integral equation formulation and its solution. Thus, the charge densities involving the fringe effects on the plates are obtained by means of analytical regularization method (ARM) constructed for annular strips earlier. The efficiency of the constructed method is demonstrated with respect to the direct integral equation solvers implemented via the entire domain Galerkin method and point matching. The main physical characteristics of the suggested system and their deviation from that of infinitely large plane approximation are discussed.

PDF

___

[1] Bourouina T, Bosseboeuf A, Grandchamp J P. Design and simulation of an electrostatic micropump for drug delivery applications. Journal of Micromechanics and Microengineering 1999; 7 (3): 186–188. doi: 10.1088/0960- 1317/16/11/028
[2] Mahija K, Pushpalatha BG, Jijesh JJ. MEMS based drug delivery system using micropump. International Journal of Electronics Signals and Systems (IJESS) 2013; 2 (3): 211-215. doi:10.47893/IJESS.2013.1108
[3] Cobo A, Sheybani R, Meng E. MEMS: Enabled drug delivery systems. Advanced Healthcare Materials 2015; 47 (7):969-982. doi: 10.1002/adhm.201400772
[4] Nisar A, Afzulpurkar N, Mahaisavariya B, Tuantranont A. MEMS-based micropumps in drug delivery and biomedical applications. Sensors and Actuators B: Chemical 2008; 130 (2): 917–942.10 doi:10.1016/j.snb.2007.10.064
[5] Zengerle R, Richter M. Simulation of microfluid systems. Journal of Micromechanics and Microengineering 1999; 412 (4): 192-204. doi: 10.1088/0960-1317/4/4/004
[6] Nemirovsky Y, Degani OB. A methodology and model for the pull-in parameters of electrostatic actuators. Journal of Microelectromechanical Systems 2001; 10 (4): 601-615. doi:10.1109/84.967384
[7] Maithripala DHS, Berg JM, Dayawansa WP. Control of an electrostatic MEMS using static and dynamic output feedback. Journal of Dynamic Systems Measurement and Control 2004; 127 (3): 443-450. doi:10.1115/1.1985443
[8] Panin S, Smith PD, Vinogradova ED, Tuchkin Yu A, Vinogradov SS. Regularization of the Dirichlet problem for Laplace’s equation: surfaces of revolution. Electromagnetics, Taylor & Francis Online 2009; 29: 53–76.19 doi:10.1080/02726340802529775
[9] Tuchkin Yu A, Panin S, Efe İ, Dikmen F, Ünal İ et al. Electrostatic Problem for Toroid Surfaces; Analytical Regularization, 2021 International Applied Computational Electromagnetics Society (ACES) Online-Live, Interactive Symposium, August 1-5, doi: 10.1109/ACES53325.2021.00045
[10] Liu YJ. Dual BIE approaches for modeling electrostatic MEMS problems with thin beams and accelerated by the fast multipole method. Engineering Analysis with Boundary Elements 2006; 30 (11): 940– 948.22 doi:10.1016/j.enganabound.2006.04.010
[11] Gibson Walton C. The Method of Moments in Electromagnetics 3rd Ed, CRC Press
[12] Popov G. Ya. On the method of orthogonal polynomials in contact problems of the theory of elasticity. Journal of Applied Mathematics and Mechanic 1969; 33 (3): 503-517. doi:10.1016/0021-8928(69)90065-3
[13] Popov G. Ya. The axisymmetric mixed problem in the theory of elasticity for a hallow truncated circular cone. Journal of Applied Mathematics and Mechanics 2000; 64 (3): 413-424. doi:10.1016/S0021-8928(00)00064-2
[14] Tuchkin Yu A. On the Analytical Regularization Method in scattering and diffraction. In: Kobayashi K and Smith P D (editors). Advances in Mathematical Methods for Electromagnetics; Chapter 13 SciTech Publishing, 2020
[15] Vinogradov S, Smith P, Vinogradova E. Canonical problems in scattering and potential theory Part I: Canonical structures in Potential theory (Chapman & Hall/CRC, Boca Raton, FL, 2002).
[16] Nosich AI. The method of analytical regularization in wave-scattering and eigenvalue problems: Foundations and review of solutions. IEEE Antennas and Propagation Magazine 1999;41 (3):34.
[17] Tuchkin Yu A. Wave scattering by open cylindrical screens of arbitrary profile with Dirichlet boundary conditions. Soviet Physics Doklady 1985;30 (12):1027
[18] Butler CM. General Solutions of the Narrow Strip (and Slot) Integral Equations.- IEEE Transactions on Antennas and Propagation, Vol. AP-33, No. 10, October 1985
[19] Poyedinchuk Ye, Tuchkin Yu A, Shestopalov VP. , New Numerical – Analytical Methods in Diffraction Theory, Mathematical and Computer Modeling, Vol 32, 2000, 1029-1046
[20] Yiğit, H.; Dikmen, F. Analytical Regularization Method for Rigorous Diffraction Analysis of Knife Edges for TM Waves. Math. Comput. Appl. 2011, 16, 738-747. https://doi.org/10.3390/mca16030738
[21] Dikmen F, Karacuha E, Tuchkin Yu A. Scalar Wave Diffraction by a Perfectly Soft Infinitely Thin Circular Ring. Turkish Journal of Electrical Engineering and Computer Science 2001; 9 (2): 199-220
[22] Ozkan E, Dikmen F, Tuchkin Yu A. Scalar Wave Diffraction by Perfectly Soft Thin Circular Cylinder of Finite Length; Analytical Regularization Method, Elektrik, Turkish Journal of Electrical Engineering and Computer Science, Tubitak Doga Series, Vol 10, 2002, 459-472
[23] Dikmen F, Tuchkin Yu A. Analytical regularization method for electromagnetic wave diffraction by axially symmetrical thin annular strips, Turk J Elec Eng & Comp Sci, Vol.17, No.2, 2009, Tubitak, doi:10.3906/elk-0811-10
[24] Amirouche F, Zhou Y, Johnson T. Current Micropump Technologies and Their Biomedical Applications. Microsystem Technologies 2009; 15 (5): 647-666. doi:10.1007/s00542-009-0804-7
[25] Francais O, Dufour I, Sarraute E. Analytical static modelling and optimization of electrostatic micropumps. Journal of Micromechanics and Microengineering 1997; 7 (3): 183–185. doi:10.1088/0960-1317/7/3/027
[26] Cheng D. Field and Wave Electromagnetics 2nd Ed, Addison Wesley
[27] Colton D, Kress R. Integral Equation Methods in Scattering Theory.-Wiley, 1983.
[28] Cohl HS, Rau ARP, Browne DA, Tohline JE, Barnes EI et al. Useful alternative to the multipole expansion of 1/r potentials. Physical Review A 2001; 64 (5): doi:10.1103/PhysRevA.64.052509
[29] Vasiliev EN. Excitation of bodies of revolution, Moscow: Radio and Communication 1987; [in Russian]
[30] Nikiforov AF, Uvarov VB. Special Functions of Mathematical Physics 1988; Birkhauser