A study of the rheological properties of visco-elastic materials using fractional calculus

摘要: Abstract We present a study of the rheological properties some visco-elastic materials biological origin and an aqueous gel synthetic clay Laponite. The bacterial biofilms are (a) Staphylococcus epidermidis, (b) Pseudomonas aeruginosa, (c) Bacillus subtilis. model these using variations three-element show that use fractional calculus incorporating non-integer time derivatives in equations, provides most appropriate framework for such study. Using single set parameters, complex modulus, creep compliance modulus viscosity, have been calculated systems under compared with available experimental results. Laponite is modeled by Boltzmann model, while 3-element fluid model. Replacing order derivative equations integer completely reverses theoretically predicted behaviour from result. conclude incorporation linear essential technique modeling over wide range frequency scales.