Slip and hall current effects on Jeffrey fluid suspension flow in a peristaltic hydromagnetic blood micropump

The magnetic properties of blood allow it to be manipulated with an electromagnetic field. Electromagnetic blood flow pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. Blood is a complex multi-phase suspension with non-Newtonian characteristics which are significant in micro-scale transport. Motivated by such applications, in the present article a mathematical model is developed for magnetohydrodynamic (MHD) pumping of blood in a deformable channel with peristaltic waves. A Jeffery’s viscoelastic formulation is employed for the rheology of blood. A twophase fluid-particle (“dusty”) model is utilized to better simulate suspension characteristics (plasma and erythrocytes). Hall current and wall slip effects are incorporated to achieve more realistic representation of actual systems. A two-dimensional asymmetric channel with dissimilar peristaltic wave trains propagating along the walls is considered. The governing conservation equations for mass, fluid and particle momentum are formulated with appropriate boundary conditions. The model is simplified using of long wavelength and creeping flow approximations. The model is also transformed from the fixed frame to the wave frame and rendered non-dimensional. Analytical solutions are derived. The resulting boundary value problem is solved analytically and exact expressions are derived for the fluid velocity, particulate velocity, fluid/particle fluid and particulate volumetric flow rates, axial pressure gradient, pressure rise and skin friction distributions are evaluated in detail. Increasing Hall current parameter reduces bolus growth in the channel, particle phase velocity and pressure difference in the augmented pumping region whereas it increases fluid phase velocity, axial pressure gradient and pressure difference in the pumping region. Increasing the hydrodynamic slip parameter accelerates both particulate and fluid phase flow at and close to the channel walls, enhances wall skin friction, boosts pressure difference in the augmented pumping region and increases bolus magnitudes. Increasing viscoelastic parameter (stress relaxation time to retardation time ratio) decelerates the fluid phase flow, accelerates the particle phase flow, decreases axial pressure gradient, elevates pressure difference in the augmented pumping region and reduces pressure difference in the pumping region. Increasing drag particulate suspension parameter decelerates the particle phase velocity, accelerates the fluid phase velocity, strongly elevates axial pressure gradient and reduces pressure difference (across one wavelength) in the augmented pumping region. Increasing particulate volume fraction density enhances bolus magnitudes in both the upper and lower zones of the channel and elevates pressure rise in the augmented pumping region

Engineering viscoelasticity

Engineering Viscoelasticity covers all aspects of the thermo- mechanical response of viscoelastic substances that a practitioner in the field of viscoelasticity would need to design experiments, interpret test data, develop stress-strain models, perform stress analyses, design structural components, and carry out research work. The material in each chapter is developed from the elementary to the advanced, providing the background in mathematics and mechanics that are central to understanding the subject matter being presented. The book examines how viscoelastic materials respond to the application of loads, and provides practical guidelines to use them in the design of commercial, military and industrial applications. This book also: ·         Facilitates conceptual understanding by progressing in each chapter from elementary to challenging material ·         Examines in detail both differential and integral constitutive equations, devoting full chapters to each type and using both forms in applications throughout the book ·         Presents variational principles and energy theorems from a practical point of view, using these to develop computational tools such as the viscoelastic equivalent of the Unit-Load and the Unit-Displacement theorems ·         Provides more than 50 examples, solved in detail, and complete solution guides (hints) to all assigned problems. ·         Features code segments to curve-fit WLF time-temperature shift and Dirichlet-Prony functions, and a computer application to obtain the convolution inverse of Prony series.  Engineering Viscoelasticity is as ideal book for first graduate-level courses on viscoelasticity, upper-level undergraduate level courses in engineering, and practicing professionals

Single-Specimen Technique to Establish the J-Resistance of Linear Viscoelastic Solids with Constant Poisson's Ratio

A method is developed to establish the J-resistance function for an isotropic linear viscoelastic solid of constant Poisson's ratio using the single-specimen technique with constant-rate test data. The method is based on the fact that, for a test specimen of fixed crack size under constant rate, the initiation J-integral may be established from the crack size itself, the actual external load and load-point displacement at growth initiation, and the relaxation modulus of the viscoelastic solid, without knowledge of the complete test record. Since crack size alone, of the required data, would be unknown at each point of the load-vs-load-point displacement curve of a single-specimen test, an expression is derived to estimate it. With it, the physical J-integral at each point of the test record may be established. Because of its basis on single-specimen testing, not only does the method not require the use of multiple specimens with differing initial crack sizes, but avoids the need for tracking crack growth as well