Rheology Field of study: Biophysics
Programme code: W4-S2BFA21.2022

1) The viscosity of liquids: introduction to rheology 2) Flow and deformation: introduction; shear rate and shear stress; dimensions and units 3) The newtonian liquid: viscosity; variation of viscosity with temperature; effects of pressure; limit of newtonian behaviour 4) Some equations for the flow of newtonian liquid: flow in rotational viscometer; flow in straight circular pipes; spheres falling in newtonian liquids; other important flows 5) Viscometry: some important things about using viscometers; viscometer design. 6) Shear—thinning liquid: qualitative features of flow curves; mathematical description of flow curves: models 7) Equations for the flow of non – newtonian fluids: some selected examples 8) Yield stress fluids: history of the yield stress and yield stress values; flow equations with yield stress 9) The flow of “solids”: non-linear “viscosity” of solids 10) Linear viscoelasticity and time effects: introduction; mechanical analogues of viscoelastic behaviour; measuring linear viscoelasticity : creep and oscillatory tests, response of model materials and real systems; relationship between oscillatory and steady-state viscoelastic parameters; stress relaxation testing and start-up experiments. 11) Non- linear viscoelasticity: everyday elastic liquids; some visible viscoelastic manifestations; proper description of viscoelastic forces and their measurements; some viscoelastic formulas 15) The flow of suspensions: viscosity of dispersions and emulsions; effects of the shape and size of the particles; overview of particle interactions; viscosity of flocculated systems; thixotropy; shear thickening 16) Polymer rheology: different kinds of polymer chains; polymer solutions; polymer melts 17) Rheology of surfactant systems: surfactant phases; rheology of surfactant systems 18) Rheology of food products 19) Extensional flow: the extensional flow; the Trouton ratio; examples of extensional viscosity curves; some applications 20) Recall on scalars, vectors, tensors and their algebra. 21) The stress tensor. Construction, property. 22) Stress ellipsoid. The case of pressure. Deformation tensor. 23) Generalized Hooke's law. Matrix of modules and compliance, its properties. Recalls: differential operators on scalars / vectors / tensors, useful theorems. 24) Conservation of the moment and the mass. Newtonian constitutive equations. Navier Stokes equation. Problems on the flow of incompressible Newtonian fluids: entrainment, f. of poiseuille, f. torsional 25) Material functions and experimental response to steady state flow in simple shear geometry and in extensional geometry. 26) Viscoelasticity and constitutive equations 27) Non-linear viscoelasticity. Cauchy and Finger Tensors. 28) Introduction to more advanced constitutive equations. Models: Integral Lodge, Maxwell Upper / Lower Convected, Cauchy-Maxwell, Rubberlike Liquid Lodge. Quasi-linear models (fluid A and B), non-linear differentials (Oldroyd 8 const.) 29) Other constitutive approaches: molecular approach for polymeric systems. Outline: Configuration distribution function, temporary network model, reptation theory

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