317 research outputs found
Characterization of High Oleic Acid Biodiesel: Improving Biofuel Properties
In 2016, the world produced an amount of biofuel equivalent to 82,306,000 tonnes of oil. A portion of the biofuels produced was categorized as biodiesel. While still growing as a fuel alternative, current biodiesel fuels are at risk for causing increased engine coking, lower engine performance and durability, oil ring sticking, carbon deposits, and gelling of lubricating oil. Due to these primary issues, biodiesel cannot completely replace petroleum diesel as a fuel source. Instead, biodiesel is commonly blended with petroleum diesel at 5% and 20% (B5 and B20) in the U.S. to create a mixture that has acceptable fuel properties. Recently, genetic modifications to soybeans have made high oleic acid soybean oil commercially available. High oleic acid soybean oil has less saturated fat and more monounsaturated fat. This characteristic is hypothesized to improve the fuel properties of biodiesel. These improvements may enable better fuel performance such that higher blends of biodiesel could be used in combustion engines around the world. The research conducted in this study aimed to test the kinematic viscosity, density, flash point, cloud point, and acid number of transesterified high oleic acid soybean oil in order to have a proof of concept that high oleic acid biodiesel meets standard specifications. High oleic acid biodiesel was found to have a kinematic viscosity of 4.639 mm^2/s, a density of 0.8789 g/cm^3, a flash point \u3e110 degrees Celsius, a cloud point of -1 degree Celsius, and an acid number of 0.071 mg KOH/g which meets every ASTM standard specification range
Nonextensive diffusion as nonlinear response
The porous media equation has been proposed as a phenomenological
``non-extensive'' generalization of classical diffusion. Here, we show that a
very similar equation can be derived, in a systematic manner, for a classical
fluid by assuming nonlinear response, i.e. that the diffusive flux depends on
gradients of a power of the concentration. The present equation distinguishes
from the porous media equation in that it describes \emph{% generalized
classical} diffusion, i.e. with scaling, but with a generalized
Einstein relation, and with power-law probability distributions typical of
nonextensive statistical mechanics
Moving boundary approximation for curved streamer ionization fronts: Solvability analysis
The minimal density model for negative streamer ionization fronts is
investigated. An earlier moving boundary approximation for this model consisted
of a "kinetic undercooling" type boundary condition in a Laplacian growth
problem of Hele-Shaw type. Here we derive a curvature correction to the moving
boundary approximation that resembles surface tension. The calculation is based
on solvability analysis with unconventional features, namely, there are three
relevant zero modes of the adjoint operator, one of them diverging;
furthermore, the inner/outer matching ahead of the front has to be performed on
a line rather than on an extended region; and the whole calculation can be
performed analytically. The analysis reveals a relation between the fields
ahead and behind a slowly evolving curved front, the curvature and the
generated conductivity. This relation forces us to give up the ideal
conductivity approximation, and we suggest to replace it by a constant
conductivity approximation. This implies that the electric potential in the
streamer interior is no longer constant but solves a Laplace equation; this
leads to a Muskat-type problem.Comment: 22 pages, 6 figure
Thermostatistics of overdamped motion of interacting particles
We show through a nonlinear Fokker-Planck formalism, and confirm by molecular
dynamics simulations, that the overdamped motion of interacting particles at
T=0, where T is the temperature of a thermal bath connected to the system, can
be directly associated with Tsallis thermostatistics. For sufficiently high
values of T, the distribution of particles becomes Gaussian, so that the
classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures
of the thermal bath, the system displays a mixed behavior that follows a novel
type of thermostatistics, where the entropy is given by a linear combination of
Tsallis and Boltzmann-Gibbs entropies.Comment: 4 pages, 2 figure
Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
A general type of nonlinear Fokker-Planck equation is derived directly from a
master equation, by introducing generalized transition rates. The H-theorem is
demonstrated for systems that follow those classes of nonlinear Fokker-Planck
equations, in the presence of an external potential. For that, a relation
involving terms of Fokker-Planck equations and general entropic forms is
proposed. It is shown that, at equilibrium, this relation is equivalent to the
maximum-entropy principle. Families of Fokker-Planck equations may be related
to a single type of entropy, and so, the correspondence between well-known
entropic forms and their associated Fokker-Planck equations is explored. It is
shown that the Boltzmann-Gibbs entropy, apart from its connection with the
standard -- linear Fokker-Planck equation -- may be also related to a family of
nonlinear Fokker-Planck equations.Comment: 19 pages, no figure
Logarithmic diffusion and porous media equations: a unified description
In this work we present the logarithmic diffusion equation as a limit case
when the index that characterizes a nonlinear Fokker-Planck equation, in its
diffusive term, goes to zero. A linear drift and a source term are considered
in this equation. Its solution has a lorentzian form, consequently this
equation characterizes a super diffusion like a L\'evy kind. In addition is
obtained an equation that unifies the porous media and the logarithmic
diffusion equations, including a generalized diffusion equation in fractal
dimension. This unification is performed in the nonextensive thermostatistics
context and increases the possibilities about the description of anomalous
diffusive processes.Comment: 5 pages. To appear in Phys. Rev.
Generalized Diffusion
The Fokker-Planck equation for the probability to find a random
walker at position at time is derived for the case that the the
probability to make jumps depends nonlinearly on . The result is a
generalized form of the classical Fokker-Planck equation where the effects of
drift, due to a violation of detailed balance, and of external fields are also
considered. It is shown that in the absence of drift and external fields a
scaling solution, describing anomalous diffusion, is only possible if the
nonlinearity in the jump probability is of the power law type (), in which case the generalized Fokker-Planck equation reduces to the
well-known Porous Media equation. Monte-Carlo simulations are shown to confirm
the theoretical results.Comment: 29 pages, 8 figure
Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition
In the selective withdrawal experiment fluid is withdrawn through a tube with
its tip suspended a distance S above a two-fluid interface. At sufficiently low
withdrawal rates, Q, the interface forms a steady state hump and only the upper
fluid is withdrawn. When Q is increased (or S decreased), the interface
undergoes a transition so that the lower fluid is entrained with the upper one,
forming a thin steady-state spout. Near this transition the hump curvature
becomes very large and displays power-law scaling behavior. This scaling allows
for steady-state hump profiles at different flow rates and tube heights to be
scaled onto a single similarity profile. I show that the scaling behavior is
independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl
Fluid Flows of Mixed Regimes in Porous Media
In porous media, there are three known regimes of fluid flows, namely,
pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are
usually treated separately in literature. To study complex flows when all three
regimes may be present in different portions of a same domain, we use a single
equation of motion to unify them. Several scenarios and models are then
considered for slightly compressible fluids. A nonlinear parabolic equation for
the pressure is derived, which is degenerate when the pressure gradient is
either small or large. We estimate the pressure and its gradient for all time
in terms of initial and boundary data. We also obtain their particular bounds
for large time which depend on the asymptotic behavior of the boundary data but
not on the initial one. Moreover, the continuous dependence of the solutions on
initial and boundary data, and the structural stability for the equation are
established.Comment: 33 page
Absence of squirt singularities for the multi-phase Muskat problem
In this paper we study the evolution of multiple fluids with different
constant densities in porous media. This physical scenario is known as the
Muskat and the (multi-phase) Hele-Shaw problems. In this context we prove that
the fluids do not develop squirt singularities.Comment: 16 page
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