Rheological effects of biomimetic propulsion on fluid flow: An application of bio-engineering

Abstract.

In the current article, we have studied few rheological phenomena related to the fluid transportation in various forms of flow geometries and motion of the fluid based upon the peristaltic propulsions of the boundary walls. This study is productive for mechanical engineers to design devices that are used as a remedy of complex cardiovascular treatments. This study deals with the flow of a viscous fluid through the complex paths due to the biomimetic propulsions of the boundary walls of geometries. Firstly, due to the complex nature of flow regimes, the continuity and momentum equations are governed into the form of curvilinear coordinates. Secondly, the governing equations are transformed from the laboratory frame to the wave frame by introducing a linear mathematical relation between these two frames. Thirdly, similarity transformations are utilized to convert the system of equations into the dimensionless form and at the last, these equations will reduce into the four ODEs in terms of stream function after using long wavelength approximation. The analytical solution of the governing equation is acquired by applying integration rules and mathematical values of integrating constants are obtained by using Mathematica 10 software. The significant impacts of physical parameters such as curvature parameter and non-uniform parameter in the velocity profile, pumping and trapping phenomena’s are argued expansively through graphs to the various forms of flow regimes. Physical characteristics of simple wavy walls and complex wavy walls of the curved channels are also highlighted in detail in the wave frame of reference. Moreover, a comparison among the straight channel and the curved channel is also emphasized. The results of the current study may be useful in designing the complex instruments which are used in medical engineering and treatment of physiological systems. Comprehensive information about the transportation of bio-fluids in the uniform as well as non-uniform vessels or arteries is obtained from the present study. This study provides dynamic information, to the mechanical engineers, to enhance the performance of the peristaltic micro-pumps.