**Arshad Riaz 1,\*, Hanan A. Al-Olayan 2, Ahmad Zeeshan 3, Abdul Razaq <sup>1</sup> and Muhammad Mubashir Bhatti <sup>4</sup>**


Received: 17 September 2018; Accepted: 13 November 2018; Published: 16 November 2018

**Abstract:** This article aims to model two-dimensional, incompressible asymmetric peristaltic propulsion coated with Synovial fluid ("non-Newtonian model") with mass transport. Due to the coating of the same base-fluid at the surface of the channel, the boundaries become non-porous and exert no slip on the fluid particles. Two illustrative models for the viscosity, namely, shear-thinning (Model 1) and shear-thickening (Model 2), are considered, which reveal the presence and integrity of coating. The perturbation method has been applied to linearize the complicated differential equations. Model 1 predicted higher viscosity values and more significant non-Newtonian behavior than Model 2. It is also observed that the shear-thinning model behaved in quite the opposite manner for the shear thickening model. The converse behavior of Models 1 and 2 occurs due to a curvature of the flow domain. Moreover, Model 1 is not able to capture the correct exponential viscosity dependence on concentration for the whole range of shear rates. On the other hand, the second model shows a strong relationship with accurate power. Solutions are attained for velocity field, concentration profile, and pressure gradient. The novelty of all the essential parameters is analyzed through graphical results. Furthermore, streamlines are also drawn to determine the trapping mechanism. The present analysis is beneficial in the study of intrauterine fluid dynamics; furthermore, it is applicable in vivo diagnostic; drug delivery; food diagnostics; protein chips; and cell chips and packaging, i.e., smart sensors.

**Keywords:** Synovial fluid; coating; shear-thinning and -thickening models; mass transport; asymmetric channel; analytical solution
