The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and...

A high molecular polymer solution with viscoelasticity has the effect of reducing frictional drag, which is quite practical for energy saving. Effective simulations viscoelastic flows in a pipeline Reynolds number realized by incorporating constitutive equation into k−ε−v′2¯−f turbulence model. The Finitely Extensive Nonlinear Elastic Peterlin (FENE-P) model employed characterizing viscoelastic...

The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution o...

The main concern of this paper is to analyze the nonlinearity Grashof numbers (thermal and diffusion) on Williamson fluid flow across a stretching sheet with non-uniform thickness consideration melting heat transfer. modelled equations are non-dimensionalized utilization similarity transformations. We used shooting technique based Runge-Kutta 4th order method unriddle ensuing equations. Influen...

Viscoelastic flows occur widely, and numerical simulations of them are important for a range industrial applications. Simulations viscoelastic more challenging than their Newtonian counterparts due to the presence exponential gradients in polymeric stress fields, which can lead catastrophic instabilities if not carefully handled. A key development overcome this issue is log-conformation formula...

The flow of viscoelastic liquids with constant shear viscosity through symmetric sudden expansions is studied by numerical means. The geometry considered is planar and the constitutive model follows the modified FENE-CR equation, valid for relative dilute solutions of polymeric fluids. For Newtonian liquids in a 1:3 expansion we predict the result that the flow becomes asymmetric for a Reynolds...

A precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation...