Identification of trapping in a peristaltic flow: A new approach using dynamical system theory

Abstract

In this paper, we propose a new approach for the identification of characteristic peristaltic flow features such as "bolus" and "trapping." Using dynamical system analysis, we relate the occurrence of a bolus to the existence of a center (an elliptic equilibrium point). Trapping occurs when centers exist under the wave crests along with a pair of saddles (hyperbolic equilibrium points) lying on the central line. For an augmented flow, centers form under the wave crests, whereas saddles lie above (below) the central line. The proposed approach works much better than the presently adopted approach in two ways: (1) it does not require random testing and (2) it characterizes the qualitative flow behavior for the complete range of parameter values. The literature is somewhat inconsistent with regard to the terminologies used for describing characteristic flow behaviors. We have addressed this issue by explicitly defining quantities such as "bolus," "backward flow," "trapping," and "augmented flow."