Encyclopedia of Microfluidics and Nanofluidics

Living Edition
| Editors: Dongqing Li

Boundary-Element Method in Microfluidics

Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27758-0_121-6

Definition

The boundary element method (BEM) is a numerical method for solving partial differential equations which are encountered in many engineering disciplines such as solid and fluid mechanics, electromagnetics, and acoustics.

Overview

Boundary element method (or boundary integral method) is a numerical tool that is well applied to many linear problems in engineering. There are several advantages of the boundary element method (BEM) over other numerical methods (such as finite element method (FEM)) and some of which are (i) discretization and modeling of only the boundary of the solution domain, (ii) improved solutions in stress concentration problems, (iii) accuracy of the solution regarding that it is a semi-analytical method (the integral equation is obtained using exact solution of the corresponding linear problem; the numerical approach is necessary only for evaluating the resulting integrals), and (iv) the...

This is a preview of subscription content, log in to check access.

References

1. 1.
Wrobel LC (2002) Boundary element method. Applications in thermo-fluids and acoustics, vol 1. Wiley, ChichesterGoogle Scholar
2. 2.
Youngreen GK, Acrivos A (1975) Stokes flow past a particle of arbitrary shape: a numerical method of solution. J Fluid Mech 69:377–403
3. 3.
Youngreen GK, Acrivos A (1976) On the shape of a gas bubble in a viscous extensional flow. J Fluid Mech 76:433–442
4. 4.
Rallison JM, Acrivos A (1978) A numerical study of the deformation and burst of a viscous drop in an extensional flow. J Fluid Mech 89:191–200
5. 5.
Lee SH, Leal LG (1982) The motion of a sphere in the presence of a deformable interface. Part 2: numerical study of the translation of a sphere normal to an interface. J Colloid Interface Sci 87:81–106
6. 6.
Al Quddus N, Moussa WA, Bhattacharjee S (2008) Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian–Eulerian method. J Colloid Interface Sci 17:20–630Google Scholar
7. 7.
Ai Y, Joo SW, Jiang Y, Xuan X, Qian S (2009) Pressure-driven transport of particles through a converging–diverging microchannel. Biomicrofluidics 3:022404
8. 8.
Çetin B, Li D (2011) Dielectrophoresis in microfluidics technology. Electrophoresis 32:2410–2427, Special issue on dielectrophoresis
9. 9.
Bruus H (2008) Theoretical microfluidics. Oxford University Press, New YorkGoogle Scholar
10. 10.
House DL, Luo H (2010) Electrophoretic mobility of a colloidal cylinder between two parallel walls. Eng Anal Bound Elem 34(5):471–476
11. 11.
House DL, Luo H (2011) Effect of direct current dielectrophoresis on the trajectory of a non-conducting colloidal sphere in a bent pore. Electrophoresis 32:3277–3285 