695 research outputs found
The thinning of the liquid layer over a probe in two-phase flow
The draining of the thin water film that is formed between a two dimensional, infinite, initially flat oil-water interface and a smooth, symmetric probe, as the interface is advected by a steady and uniform flow parallel to the probe axis, is modelled using classical fluid dynamics.
The governing equations are nondimensionalised using values appropriate to the oil extraction industry. The bulk flow is driven by inertia and, in some extremes, surface tension while the viscous effects are initially confined to thin boundary layers on the probe and the interface. The flow in the thin water film is dominated by surface tension, and passes through a series of asymptotic regimes in which inertial forces are gradually overtaken by viscous forces. For each of these regimes, and for those concerning the earlier stages of approach, possible solution strategies are discussed and relevant literature reviewed.
Consideration is given to the drainage mechanism around a probe which protrudes a fixed specified distance into the oil. A lubrication analysis of the thin water film may be matched into a capillary-static solution for the outer geometry using a slender transition region if, and only if, the pressure gradient in the film is negative as it meets the static meniscus. The remarkable result is that, in practice, there is a race between rupture in the transition region and rupture at the tip. The analysis is applicable to the case of a very slow far field flow and offers significant insight into the non-static case.
Finally, a similar approach is applied to study the motion of the thin water film in the fully inviscid approximation, with surface tension and a density contrast between the fluids
On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions
We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions
A spectral boundary integral method for inviscid water waves in a finite domain
In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite depth with a spatially varying bottom. In each case, we use Chebyshev polynomials as the basis of our representation of the solution and filtering to remove spurious high-frequency modes. We show that spectral accuracy can be achieved until wave breaking, plunging or wall impingment occurs in two model problems
Slip or not slip? A methodical examination of the interface formation model using two-dimensional droplet spreading on a horizontal planar substrate as a prototype system
We consider the spreading of a thin two-dimensional droplet on a planar
substrate as a prototype system to compare the contemporary model for contact
line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas.
Flow 19, 589 (1993)], to the more commonly used continuum fluid dynamical
equations augmented with the Navier-slip condition. Considering quasistatic
droplet evolution and using the method of matched asymptotics, we find that the
evolution of the droplet radius using the interface formation model reduces to
an equivalent expression for a slip model, where the prescribed microscopic
dynamic contact angle has a velocity dependent correction to its static value.
This result is found for both the original interface formation model
formulation and for a more recent version, where mass transfer from bulk to
surface layers is accounted for through the boundary conditions. Various
features of the model, such as the pressure behaviour and rolling motion at the
contact line, and their relevance, are also considered in the prototype system
we adopt.Comment: 45 pages, 18 figure
The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary
Using a thermodynamic approach based upon the fluctuation-dissipation theorem
we quantify the stochastic dynamics of rectangular and V-shaped microscale
cantilevers immersed in a viscous fluid. We show that the stochastic cantilever
dynamics as measured by the displacement of the cantilever tip or by the angle
of the cantilever tip are different. We trace this difference to contributions
from the higher modes of the cantilever. We find that contributions from the
higher modes are significant in the dynamics of the cantilever tip-angle. For
the V-shaped cantilever the resulting flow field is three-dimensional and
complex in contrast to what is found for a long and slender rectangular
cantilever. Despite this complexity the stochastic dynamics can be predicted
using a two-dimensional model with an appropriately chosen length scale. We
also quantify the increased fluid dissipation that results as a V-shaped
cantilever is brought near a solid planar boundary.Comment: 10 pages, 15 images, corrected equation (8
Dynamics and pattern formation in invasive tumor growth
In this work, we study the in-vitro dynamics of the most malignant form of
the primary brain tumor: Glioblastoma Multiforme. Typically, the growing tumor
consists of the inner dense proliferating zone and the outer less dense
invasive region. Experiments with different types of cells show qualitatively
different behavior. Wild-type cells invade a spherically symmetric manner, but
mutant cells are organized in tenuous branches. We formulate a model for this
sort of growth using two coupled reaction-diffusion equations for the cell and
nutrient concentrations. When the ratio of the nutrient and cell diffusion
coefficients exceeds some critical value, the plane propagating front becomes
unstable with respect to transversal perturbations. The instability threshold
and the full phase-plane diagram in the parameter space are determined. The
results are in a good agreement with experimental findings for the two types of
cells.Comment: 4 pages, 4 figure
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