title: Peristaltic propulsion of generalized Burgers' fluids through a non-uniform porous medium: a study of chyme dynamics through the diseased intestine.
abstract: A mathematical study of the peristaltic flow of complex rheological viscoelastic fluids using the generalized fractional Burgers' model through a non-uniform channel is presented. This model is designed to study the movement of chyme and undigested chyme (biophysical waste materials) through the small intestine to the large intestine. To simulate blockages and impedance of debris generated by cell shedding, infections, adhesions on the wall and undigested material, a drag force porous media model is utilized. This effectively mimicks resistance to chyme percolation generated by solid matrix particles in the regime. The conduit geometry is mathematically simulated as a sinusoidal propagation with linear increment in shape of the bolus along the length of channel. A modified Darcy-Brinkman model is employed to simulate the generalized flows through isotropic, homogenous porous media, a simplified but physically robust approximation to actual clinical situations. To model the rheological properties of chyme, a viscoelastic Burgers' fluid formulation is adopted. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. Numerical and approximate analytical solutions are obtained with two semi-numerical techniques, namely the homotopy perturbation method and the variational iteration method. Visualization of the results is achieved with Mathematica software. The influence of the dominant hydromechanical and geometric parameters such as fractional viscoelastic parameters, wave number, non-uniformity constant, permeability parameter, and material constants on the peristaltic flow characteristics are depicted graphically.
authors.affiliation: Department of Mathematics, National Institute of Technology Delhi, Delhi 110077, India. Electronic address: dtripathi.rs.apm@itbhu.ac.in.
authors.forename: D
authors.initials: D
authors.lastname: Tripathi
authors.affiliation: Gort Engovation Research (Propulsion, Nanomechanics, and Biophysics), Southmere Ave., Bradford BD73NU, UK.
authors.forename: O
authors.initials: O
authors.lastname: Anwar Bég
mesh_terms: D055592:Biophysical Phenomena; D001826:Body Fluids / Q000502:physiology; D004548:Elasticity; D005766:Gastrointestinal Contents; D006801:Humans; D007410:Intestinal Diseases / Q000503:physiopathology*; D055641:Mathematical Concepts; D008954:Models, Biological; D010528:Peristalsis / Q000502:physiology*; D016062:Porosity; D012212:Rheology; D014783:Viscosity
keywords: Digestive transport; Fractional calculus; Homotopy perturbation method; Peristaltic propulsion waves; Variational iteration method; Viscoelastic fluids