Page 473 - Handbook of Biomechatronics

Bioinspired and Biomimetic Micro-Robotics for Therapeutic Applications 467

numerical problem, the solution could be quite costly in terms of time and
computational resources. Unfortunately, the nonlinear nature of the fluid
dynamics problem at hand does not allow most of the numerical tools to
be used for fast and cheap calculations let alone real-time control. On top
of that, a powerful computational tool, either a commercial package or a
custom code, is inevitably required to investigate the hydrodynamics of
micro-swimmers with higher accuracy for micro-robotic research.
It is important to concisely acknowledge the numerical methods,
namely the computational fluid dynamics (CFD), used to further under-
stand the hydrodynamics of the problem that calls for considerable
computational power to resolve higher-order effects taking place during
the momentum transfer from a micro-swimmer to the surrounding liquid.
CFD methods can be primarily categorized into three main branches:
(i) finite element method (FEM), with which either full Navier-Stokes
equations or only Stokes equations, subject to continuity, are solved with
discretizing the entire domain occupied by the liquid (Tabak and
Yesilyurt, 2014a); (ii) boundary element method (BEM), with which only
boundaries are discretized and the flow field is predicted by mathematical
functions such as Stokeslet functions (Phan-Thien et al., 1987); and
(iii) immersed boundary (IB) method, with which the internal structural
stresses are coupled with the fluid stresses at the boundary that is discretized
as presented by Maniyeri et al. (2012), and the authors utilized the finite
volume method (FVM) instead of FEM to discretize the domain. In the
FEM analysis, boundary conditions are set as “no-slip” for stationary solid
boundaries, “velocity vector” for moving boundaries, and the main constit-
uents of the solution are the viscous force on boundaries, velocity in the
bulk of the liquid, and pressure profile in the entire domain (Tabak and
Yesilyurt, 2014a) (see Fig. 3). The details of and differences between
FEM and FVM are left to the reader to investigate.
Indeed, many more modeling studies are present in the literature. At this
juncture, the reader should focus the attention on the fact that numerical
analysis is invaluable to examine the hydrodynamic interactions.
Ascertaining the hydrodynamic interactions between solid boundaries and
the micro-swimmer (Fauci and McDonald, 1995), within flagella bundles
(Flores et al., 2005), or between body and tail of a micro-swimmer
(Tabak and Yesilyurt, 2014a) is crucial for gait planning and robust robot
control. It should be also noted that mathematicians demonstrated the impli-
cation of these secondary effects with delicate methods (Lighthill, 1996);
however, the analysis gets rather laborious, and sometimes to the point of