Related papers: Circular hydraulic jump in generalized-Newtonian f…
In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under the influence of an externally applied temperature gradient. The outer fluid is modelled by the…
We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary…
The creeping flow of a generalized Newtonian fluid in a non--uniform pore throat is investigated analytically. The analytical solution determines the flow regimes and the transition point from Newtonian to the power law flow regime. As an…
As stated in the title, the present research proposes a mathematical definition of laminar and turbulent flows, i.e., a definition that may be used to conceive and prove mathematical theorems about such flows. The definition is based on an…
In this paper, we derive consistent shallow water equations for bi-layer flows of Newtonian fluids flowing down a ramp. We carry out a complete spectral analysis of steady flows in the low frequency regime and show the occurence of…
We investigate the steady-state fluid--structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a…
We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…
This work is concerned with our recently developed formalism of non-equilibrium thermodynamics. This formalism extends the classical irreversible thermodynamics which leads to classical thermodynamics and can not describe physical phenomena…
We analyse a generalisation of Z\"{o}ttl and Stark's model of active spherical particles [Phys. Rev. Lett. 108, 218104 (2012)] and prolate spheroidal particles [Eur. Phys. J. E 36(1), 4 (2013)] suspended in cylindrical Poiseuille flow, to…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
We consider a system of nonlinear partial differential equations modeling the unsteady motion of an incompressible generalized Newtonian fluid with chemical reactions. The system consists of the generalized Navier-Stokes equations with…
A thermal colloid suspended in a liquid will transition from a short time ballistic motion to a long time diffusive motion. However, the transition between ballistic and diffusive motion is highly dependent on the properties and structure…
We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments,…
This paper is concerned with steady, fully developed motion of a Navier-Stokes fluid with shear-dependent viscosity in a curved pipe under a given axial pressure gradient. We establish existence and uniqueness results, derive appropriate…
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…
In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid model is a well-known non-Newtonian model, with two parameters:…
We analyze gradient flows with jumps generated by a finite set of complete vector fields in involution using some Radon measures $u\in \mathcal{U}_a$ as admissible perturbations. Both the evolution of a bounded gradient flow $\{x^u(t,\l)\in…
This is a fluid dynamics video of two- and three-dimensional computational fluid dynamics simulations carried out at St. Anthony Falls Laboratory. A transient hydraulic jump is simulated using OpenFOAM, an open source numerical solver. A…
This chapter on the rheology of active fluids is an attempt to correlate theoretical and experimental work. A considerable amount of theoretical work and most of the experimental data focus on the rheology of active fluids in a Newtonian…
We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). The derivation is made in the zero-shear…