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Laboratory experiments were conducted to study particle migration and flow properties of non- Brownian, non-colloidal suspensions ranging from 10% to 40% particle volume fraction in a pressure-driven flow over and through a porous structure…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We investigate a mathematical theory for the erosion of sediment which begins with the study of a non-linear, parabolic, weighted 4-Laplace equation on a rectangular domain corresponding to a base segment of an extended landscape. Imposing…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
$\text{CO}_{2}$ flooding is central to carbon utilization technologies, yet conventional waterflooding models fail to capture the complex interactions between CO$_2$ and formation fluids. In this study, one- and two-dimensional nuclear…
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
The dynamics of thin volatile droplets comprising of binary mixtures deposited on a heated substrate are investigated. Using lubrication theory, we develop a novel one-sided model to predict the spreading and retraction of an evaporating…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…
The fragmentation of small, brittle, flexible, inextensible fibers is investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such small fibers spend most of their time fully stretched and their dynamics follows that of…
Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding…
Traditionally, the deformation of continuum is divided into elastic, plastic, and flow. For a large deformation with cracking, they are combined together. So, for complicated deformation, a formulation to express the evolution of…
Robust radiative transfer techniques are requisite for efficiently extracting the physical and chemical information from molecular rotational lines.We study several hypotheses that enable robust estimations of the column densities and…
Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that…
A theoretical framework is established to model the evaporation from continuously fed droplets, promising tools in the thermal management of high heat flux electronics. Using the framework, a comprehensive model is developed for a…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
If a porous media is being damaged by excessive stress, the elastic matrix at every infinitesimal volume separates into a 'solid' and a 'broken' component. The 'solid' part is the one that is capable of transferring stress, whereas the…