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The subject of viscoelastic flow phenomena is crucial to many areas of engineering and the physical sciences. Although much of our understanding of viscoelastic flow features stems from carefully designed experiments, preparation of model…
When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a…
We consider a transport equation by a gradient vector field with a small viscous perturbation --$\epsilon\Delta_g$. We study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit…
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves leveraging differentiability properties of the…
A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid…
In this paper, we mainly focus on the existence of the viscosity solutions of \begin{equation*} \left\{ \begin{aligned} &H_1(x,Du_1(x),u_1(x),u_2(x))=0,\\ &H_2(x,Du_2(x),u_2(x),u_1(x))=0. \end{aligned} \right. \end{equation*} The standard…
The results of experimental measurements, molecular dynamics simulation, and theoretical calculations of the viscosity of a cobalt melt in a temperature range of $1400-2000$~K at a pressure $p=1.5$~bar corresponding to an overcooled melt at…
The dynamics and rheology of a vesicle confined in a channel under shear flow are studied at finite temperature. The effect of finite temperature on vesicle motion and system viscosity is investigated. A two-dimensional numerical model,…
We consider the motion of a point mass in a one-dimensional viscous compressible barotropic fluid. The fluid--point mass system is governed by the barotropic compressible Navier--Stokes equations and Newton's equation of motion. Our main…
In the last few decades, theoretical and experimental studies of glass-forming liquids have revealed presence of universal regularities in the viscosity-temperature data. In the present work, we propose a viscosity model for scaling…
Brownian motion is the perpetual irregular motion exhibited by small particles immersed in a fluid. Such random motion of the particles is produced by statistical fluctuations in the collisions they suffer with the molecules of the…
We present a complete calculation, fully accounting for quantum effects and for molecular flexibility, of the first dielectric virial coefficient of water and its isotopologues. The contribution of the electronic polarizability is computed…
Fluid flows are typically studied by solving the Navier--Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, to be identically zero. The Stokes' hypothesis is a…
Electron hydrodynamics is an emerging framework that describes dynamics of interacting electron systems as conventional fluids. While evidence for hydrodynamic-like transport is reported in a variety of two-dimensional materials, precise…
A recent experiment has considered the effective permeability of two-phase flow of air and a water-glycerol solution under steady-state conditions in a two-dimensional model porous medium, and found a power law dependence with respect to…
Supercooling of water can be easily studied with a simple apparatus suitable for the student laboratory. We describe such an apparatus and its capabilities. The parameters influencing supercooling include the initial temperature of the…
We experimentally investigated the splashing of dense suspension droplets impacting a solid surface, extending prior work to the regime where the viscosity of the suspending liquid becomes a significant parameter. The overall behavior can…
Viscosity is a fundamental property of liquids and determines the diffusivity of suspended particles. A gradient in viscosity leads to a gradient in diffusivity, yet it is unknown whether such a gradient can lead to directed transport of…
The hypersphere model is a simple one-parameter model of the potential energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in $\mathbb{R}^{3N}$ in which $N$ is the…
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…