On Generalized Compressible Fluid Systems on an Evolving Surface with a Boundary

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a mathematical model for compressible fluid flow on the evolving surface. Moreover, we investigate the boundary conditions in co-normal direction for our fluid system to study the conservation and energy laws of the system.Comment: arXiv admin note: text overlap with arXiv:1705.0718

Center for low-gravity fluid mechanics and transport phenomena

Research projects in several areas are discussed. Mass transport in vapor phase systems, droplet collisions and coalescence in microgravity, and rapid solidification of undercooled melts are discussed

On a thermodynamic framework for developing boundary conditions for Korteweg fluids

We provide a derivation of several classes of boundary conditions for fluids of Korteweg-type using a simple and transparent thermodynamic approach that automatically guarentees that the derived boundary conditions are compatible with the second law of thermodynamics. The starting assumption of our approach is to describe the boundary of the domain as the membrane separating two different continua, one inside the domain, and the other outside the domain. With this viewpoint one may employ the framework of continuum thermodynamics involving singular surfaces. This approach allows us to identify, for various classes of surface Helmholtz free energies, the corresponding surface entropy production mechanisms. By establishing the constitutive relations that guarantee that the surface entropy production is non-negative, we identify a new class of boundary conditions, which on one hand generalizes in a nontrivial manner the Navier's slip boundary conditions, and on the other hand describes dynamic and static contact angle conditions. We explore the general model in detail for a particular case of Korteweg fluid where the Helmholtz free energy in the bulk is that of a van der Waals fluid. We perform a series of numerical experiments to document the basic qualitative features of the novel boundary conditions and their practical applicability to model phenomena such as the contact angle hysteresis

Applications of a new theory extending continuum mechanics to the nanoscale

In this dissertation, we present the Slattery-Oh-Fu theory extending continuum mechanics to the nanoscale and its applications. We begin with an analysis of supercritical adsorption of argon, krypton, and methane on Graphon before we fully develop the theory. We compare our results both with existing experimental data and with prior molecular-based theories. Then, we present the general theory, which is based upon a long history of important developments beginning with Hamaker (1937). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on PDMS. For the contact angle predictions, the results are compatible with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young??s equation for the true, rather than apparent, common line. We also studied Mode I fracture at nanoscale. While we don??t have experimental data to compare, we get reasonable crack configuration and avoid stress singularity at the crack tip. Coalescence problems are revisited to explore the retardation effects in the computation of intermolecular forces. We get good agreement with experimental results. We conclude with a confidence that this theory can be used as a bridge between continuum mechanics and other molecular-based methods

Direct numerical simulation of turbulent channel flow over porous walls

We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier--Stokes (NS) equations, while in the porous layers the Volume-Averaged Navier--Stokes (VANS) equations are used, which are obtained by volume-averaging the microscopic flow field over a small volume that is larger than the typical dimensions of the pores. In this way the porous medium has a continuum description, and can be specified without the need of a detailed knowledge of the pore microstructure by indipendently assigning permeability and porosity. At the interface between the porous material and the fluid region, momentum-transfer conditions are applied, in which an available coefficient related to the unknown structure of the interface can be used as an error estimate. To set up the numerical problem, the velocity-vorticity formulation of the coupled NS and VANS equations is derived and implemented in a pseudo-spectral DNS solver. Most of the simulations are carried out at $Re_\tau=180$ and consider low-permeability materials; a parameter study is used to describe the role played by permeability, porosity, thickness of the porous material, and the coefficient of the momentum-transfer interface conditions. Among them permeability, even when very small, is shown to play a major role in determining the response of the channel flow to the permeable wall. Turbulence statistics and instantaneous flow fields, in comparative form to the flow over a smooth impermeable wall, are used to understand the main changes introduced by the porous material. A simulations at higher Reynolds number is used to illustrate the main scaling quantities.Comment: Revised version, with additional data and more in-depth analysi

Carbon dioxide - heavy oil systems: thermodynamics, transport and interfacial stability

Conventional oil recovery leaves behind around 67% of original oil in place for light oils and all of it for heavy oils. The carbon dioxide flooding process is the cheapest among the recovery methods for the next stage. The interest here lies in recovering heavy oil. When CO2 dissolves in oil, it increases the volume of oil, squeezes it out of narrow capillaries and the viscosity of oil drops by up to an order of magnitude. Starting with the available data with and without CO2 in heavy oil, the free volume theory is used to predict these physical properties. Specific volume CO2 in the solution is obtained from the swelling data. The viscosity data show us how to obtain the free volumes of CO2 in oil and hence allow prediction of the diffusivity of CO2. Separately, an analysis of the displacement process has been undertaken in a single cylindrical pore ~ 1 µm in diameter where the disjoining pressure is included and added to the Laplace pressure, besides the correlations obtained earlier. Numerical solutions have been obtained to provide the results: profile shapes, capillary numbers, and the thickness of thin oil film left behind the drive and net mass transfer rates across the interface. Finally, the viscosity of heavy crude is much higher than the viscosity of CO2 because of which the displacement process can be unstable leading to fingering or channeling. Linear stability analysis of the displacement process which is that of immiscible displacement but includes mass transfer has been investigated. We are able to provide results that lead to a stabilizing effect overcomes a large destabilizing effect of the adverse mobility ratio. The results show that in the limit that the solubility of CO2 in oil drops to zero, the above window of instability becomes infinite --Abstract, page iii