A Nonlinear Dynamical Systems Approach to Modelling Chaotic Flow Patterns in Reused Engine Oil Under Variable Shear and Thermal Stress
Raheem, T. L.
Dosunmu G.O.
Samuel P. O.
Abstract
Recycling of engine oil is a widespread practice in Nigeria, largely driven by high costs of fresh lubricants and limited availability. While reuse reduces waste and provides short-term economic relief, the process progressively leads to viscosity loss, thermal degradation, and the accumulation of contaminants such as soot, metallic particles, and oxidation byproducts. These changes destabilize flow characteristics and compromise lubrication efficiency. To investigate this phenomenon, a mathematical framework based on nonlinear dynamical systems was developed. The model integrates the incompressible Navier–Stokes equations with a viscosity degradation law, contaminant transport, and stochastic forcing to reflect random disturbances from impurities. Thermal effects were incorporated through an energy equation to simulate harsh operating conditions typical of tropical climates. Numerical simulations were carried out using a finite-difference scheme and Euler–Maruyama integration for stochastic terms, implemented in the Dedalus framework. Results showed that reused oil exhibits a transition from laminar flow to chaotic regimes through bifurcations, particularly under high shear stress and elevated temperatures. Lyapunov exponent analysis confirmed the onset of chaos, while phase portraits revealed strange attractors characteristic of complex dynamics. An optimization routine estimated safe reuse limits, predicting maximum operation cycles of ~27 hours before instability occurs. This study highlights the critical influence of contaminants and thermal stress in triggering chaotic flow, providing theoretical guidance for safer and more sustainable lubricant management in resource-constrained environments.
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