Mixing lamellae in a shear flow

Mixing dynamics in flows are governed by the coupled action of diffusion and stretching by velocity gradients. This leads to the development of elongated lamellar structures in scalar fields where concentration fluctuations exist at scales set by the Batchelor scale. Because the latter is generally too small to be resolved experimentally, observation of these mechanisms remains an outstanding challenge. Here we present high-resolution experiments allowing for the precise quantification of the evolution of concentration distributions at the scale of a single lamella experiencing diffusion, stretching and aggregation with other lamellae. Quantitative agreement is found with analytical predictions for the lamella’s concentration profile, Batchelor time, Batchelor length scale, and concentration distribution for a large range of Péclet numbers and without adjustable parameter. This benchmark configuration is used to set the experimental spatial resolution required to quantify the concentration probability density functions (PDFs) of scalar mixtures in fluids. The diffusive coalescence of two nearby lamellae, the mechanism by which scalar mixtures ultimately reach uniformity, is shown to induce a complex transient evolution of the concentration PDFs.

The lamellar description of mixing in porous media

We develop a general framework for modelling mixing in porous media flows, in which the scalar mixture is represented as an ensemble of lamellae evolving through stretching, diffusion and coalescence. Detailed numerical simulations in Darcy scale heterogeneous permeability fields are used to analyse the lamella deformation process, which controls the local concentration gradients and thus the evolution of the concentration mixture through stretching enhanced diffusion. The corresponding Lagrangian deformation process is shown to be well modelled by a Langevin equation with multiplicative noise, which can be coupled with diffusion to predict the temporal evolution of the concentration probability density function (PDF). At late times, lamella interaction is enforced by confinement of the mixture within the dispersion area. This process is shown to be well represented by a random aggregation model, which quantifies the frequency of lamella coalescence and allows us to predict the temporal evolution of the concentration PDF in this regime. The proposed theoretical framework provides an accurate prediction of the concentration PDFs at all investigated times, heterogeneity levels and Péclet numbers. In particular, it relates the temporal behaviour of mixing, as quantified by concentration moments, scalar dissipation rate or spatial increments of concentration, to the degree of structural heterogeneity.

Assess arsenic distribution in groundwater applying GIS in capital of Punjab, Pakistan

Arsenic contamination of groundwater resources threatens the health of millions of people worldwide, particularly in the densely populated river deltas of Southeast Asia. Arsenic causes health concerns due to its significant toxicity and worldwide presence in portable water. The major sources of arsenic pollution may be natural process such as dissolution of arsenic containing minerals and anthropogenic activities. Lahore is groundwater dependent city, arsenic contamination is a major issue of portable water and has recently been most environmental health management issue especially in the plain region, where population density is very high. GIS was used in this study for visualizing distribution of arsenic groundwater concentration through geostatistics analysis technique, and exposure risk zones for two years (2010 and 2012). Town's data was compared and concentration variation evaluated. ANOVA test was also applied to compare concentration between cities and years. Arsenic concentrations widely range 7.3–67.8 and 5.2–69.3 μg L−1 in 2010 and 2012, respectively. Over 71% area is represented arsenic concentration range from 20 to 30 μg L−1 in both analyzed years. However, in 2012 arsenic concentration over 40 μg L−1 has covered 7.6% area of Data Gunjbuksh and 8.1% of Ravi Town, while over 90% area of Allama Iqbal, Aziz Bhatti and Samanabad Town contain arsenic concentration between 20–30 μg L−1. ANOVA test depicts concentration probability less than 0.05, while differences were detected among towns. In light of current results, it needs urgent step to ensure groundwater protection and preservation for future.

The diffusive strip method for scalar mixing in two dimensions

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.