Related papers: The Mixing efficiency of open flows
We study mixing and diffusion properties of passive scalars driven by $generic$ rough shear flows. Genericity is here understood in the sense of prevalence and (ir)regularity is measured in the Besov-Nikolskii scale $B^{\alpha}_{1,…
Mixing of a passive scalar in a fluid flow results from a two part process in which large gradients are first created by advection and then smoothed by diffusion. We investigate methods of designing efficient stirrers to optimize mixing of…
The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial…
Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to…
We consider the efficiency of turbulence, a dimensionless parameter that characterises the fraction of the input energy stored into a turbulent flow field. We first show that the inverse of the efficiency provides an upper bound for the…
Recent experiments suggest that shear-enhanced growth of concentration fluctuations in polymer solutions is strongly influenced by solid boundaries. We analyze the dynamics of a model of a sheared polymer solution, accounting for the effect…
We investigate experimentally the mixing dynamics in a channel flow with a finite stirring region undergoing chaotic advection. We study the homogenization of dye in two variants of an eggbeater stirring protocol that differ in the extent…
We investigate the influence of elastic turbulence on mixing of a scalar concentration field within a viscoelastic fluid in a two-dimensional Taylor-Couette geometry using numerical solutions of the Oldroyd-B model. The flow state is…
Mixing of a passive scalar in the peripheral region close to a wall is investigated by means of accurate direct numerical simulations of both a three-dimensional Couette channel flow at low Reynolds numbers and a two-dimensional synthetic…
Multiscale metrics such as negative Sobolev norms are effective for quantifying the degree of mixedness of a passive scalar field advected by an incompressible flow in the absence of diffusion. In this paper we introduce a mix norm that is…
We describe how a convectively unstable active field in an open flow configuration becomes absolutely unstable due to local mixing. A representation of the mixing region as those with locally enhanced effective diffusion allows us to find…
Consider a diffusion-free passive scalar $\theta$ being mixed by an incompressible flow $u$ on the torus $\mathbb{T}^d$. Our aim is to study how well this scalar can be mixed under an enstrophy constraint on the advecting velocity field.Our…
We consider a model of a binary mixture of two immiscible compressible fluids. We propose a numerical scheme and discuss its basic properties: Stability, consistency, convergence. The convergence is established via the method of generalized…
The optimization of the mixing of a passive scalar at finite P\'eclet number $Pe=Uh/\kappa$ (where $U,h$ are characteristic velocity and length scales and $\kappa$ is the scalar diffusivity) is relevant to many significant flow challenges…
We consider a passive scalar $f$ advected by a strictly monotone shear flow and with a diffusivity parameter $\nu\ll 1$. We prove an estimate on the homogeneous $\dot{H}^{-1}$ norm of $f$ that combines both the $L^2$ enhanced diffusion…
The problem of incompressible fluid mixing arises in numerous engineering applications and has been well-studied over the years, yet many open questions remain. This paper aims to address the question "what do efficient flow fields for…
Mixing in fluids is a rapidly developing field of fluid mechanics \cite{Sreen,Shr,War}, being an important industrial and environmental problem. The mixing of liquids at low Reynolds numbers is usually quite weak in simple flows, and it…
Recent numerical results show that if a scalar is mixed by periodically forced turbulence, the average mixing rate is directly affected for forcing frequencies small compared to the integral turbulence frequency. We elucidate this by an…
Stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not…
Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the…