592 research outputs found
Boundary elements method for microfluidic two-phase flows in shallow channels
In the following work we apply the boundary element method to two-phase flows
in shallow microchannels, where one phase is dispersed and does not wet the
channel walls. These kinds of flows are often encountered in microfluidic
Lab-on-a-Chip devices and characterized by low Reynolds and low capillary
numbers.
Assuming that these channels are homogeneous in height and have a large
aspect ratio, we use depth-averaged equations to describe these two-phase flows
using the Brinkman equation, which constitutes a refinement of Darcy's law.
These partial differential equations are discretized and solved numerically
using the boundary element method, where a stabilization scheme is applied to
the surface tension terms, allowing for a less restrictive time step at low
capillary numbers. The convergence of the numerical algorithm is checked
against a static analytical solution and on a dynamic test case. Finally the
algorithm is applied to the non-linear development of the Saffman-Taylor
instability and compared to experimental studies of droplet deformation in
expanding flows.Comment: accepted for publication, Computers and Fluids 201
Ulcers in restrained rats: Study of protective substances
The genesis of ulcers in restrained rats is discussed through an investigation of the relationship between the protective effects of nervous system effectual substances examined vis-a-vis ulcers in restrained rats and their elective or secondary pharmacologic effects. The substances used were capable of either peripheral parasympatholytic, sympatholytic, ganglioplegic, spasmolytic effects or central, hypnotic, tranquilizing, neuroleptic, analgesic effects. The regular and considerable protection observed with parasympatholytics (atropine sulfate, benzylonium bromide, dihexyverine, J.L. 1344) and a ganglioplegic (pentamethonium) is a function of their anticholinergic properties. It is of less importance with dibenamine, a sympatholytic action on the adrenergic receptors. Among the central depressive substances tested (hypnotics, tranquilizers, neuroleptics, analgesic), phenobarbital at a nonhypnotic dose, and dextromoramide at a nonanalgesic dose, show antiulcerous effects, which are found with chlorpromazine only at cataleptogenic doses
Influence of ambient temperatures on the production of restraint ulcers in the rat
A study of the influence of ambient temperature on the production of restraint ulcers in the rat is described. It concludes that the production of restrain ulcers, is favored by the reduction of the environmental temperature, whether the rat has been subjected to a fast or not
Reduction of the duration of restraint for the production of experimental ulcers in rats: Application to the study of protective substances
An experiment is described which was designed to cause ulcers in rats, but requiring less restraint time than previously used procedures. The method and results are presented
Restraint ulcers in the rat. 1: Influence on ulcer frequency of fasting and of environmental temperature associated with immobilization of varying durations
The results of the production of experimental ulcers in rats are described. Two experimental conditions were found to regularly provoke the appearance of gastric ulcers in a high percentage of rats: (1) two-and-a-half hour restraint, proceeded by a 24 hour fast; and (2) one-and-a-half hour restraint with lowering of the environmental temperature while fasting
The stability of a rising droplet: an inertialess nonmodal growth mechanism
Prior modal stability analysis (Kojima et al., Phys. Fluids, vol. 27, 1984)
predicted that a rising or sedimenting droplet in a viscous fluid is stable in
the presence of surface tension no matter how small, in contrast to
experimental and numerical results. By performing a non-modal stability
analysis, we demonstrate the potential for transient growth of the interfacial
energy of a rising droplet in the limit of inertialess Stokes equations. The
predicted critical capillary numbers for transient growth agree well with those
for unstable shape evolution of droplets found in the direct numerical
simulations of Koh & Leal (Phys. Fluids, vol. 1, 1989). Boundary integral
simulations are used to delineate the critical amplitude of the most
destabilizing perturbations. The critical amplitude is negatively correlated
with the linear optimal energy growth, implying that the transient growth is
responsible for reducing the necessary perturbation amplitude required to
escape the basin of attraction of the spherical solution.Comment: 11pages, 7 figure
Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton's theory to empirical models
The aim of this study is to derive accurate models for quantities
characterizing the dynamics of droplets of non-vanishing viscosity in
capillaries. In particular, we propose models for the uniform-film thickness
separating the droplet from the tube walls, for the droplet front and rear
curvatures and pressure jumps, and for the droplet velocity in a range of
capillary numbers, , from to and inner-to-outer viscosity
ratios, , from , i.e. a bubble, to high viscosity droplets.
Theoretical asymptotic results obtained in the limit of small capillary number
are combined with accurate numerical simulations at larger . With these
models at hand, we can compute the pressure drop induced by the droplet. The
film thickness at low capillary numbers () agrees well with
Bretherton's scaling for bubbles as long as . For larger viscosity
ratios, the film thickness increases monotonically, before saturating for
to a value times larger than the film thickness of a
bubble. At larger capillary numbers, the film thickness follows the rational
function proposed by Aussillous \& Qu\'er\'e (2000) for bubbles, with a fitting
coefficient which is viscosity-ratio dependent. This coefficient modifies the
value to which the film thickness saturates at large capillary numbers. The
velocity of the droplet is found to be strongly dependent on the capillary
number and viscosity ratio. We also show that the normal viscous stresses at
the front and rear caps of the droplets cannot be neglected when calculating
the pressure drop for
Second-order sensitivity of parallel shear flows and optimal spanwise-periodic flow modifications
The question of optimal spanwise-periodic modification for the stabilisation
of spanwise-invariant flows is addressed. A 2nd-order sensitivity analysis is
conducted for the linear temporal stability of parallel flows U0 subject to
small-amplitude spanwise-periodic modification e*U1, e<<1. Spanwise-periodic
modifications have a quadratic effect on stability, i.e. the 1st-order
eigenvalue variation is zero. A 2nd-order sensitivity operator is computed from
a 1D calculation, allowing one to predict how eigenvalues are affected by any
U1, without actually solving for modified eigenvalues/eigenmodes. Comparisons
with full 2D stability calculations in a plane channel flow and in a mixing
layer show excellent agreement. Next, optimisation is performed on the
2nd-order sensitivity operator: for each eigenmode streamwise wavenumber and
base flow modification spanwise wavenumber b, the most stabilising profiles U1
are computed, together with lower bounds for the variation in leading
eigenvalue. These bounds increase like b^-2 as b goes to 0, yielding a large
stabilising potential. However, 3D modes with wavenumbers |b0|=b and b/2 are
destabilised, thus larger control wavenumbers should be preferred. The
modification U1 optimised for the most unstable streamwise wavenumber has a
stabilising effect on other streamwise wavenumbers too. Finally, the potential
of transient growth to amplify perturbations and stabilise the flow is
assessed. Combined optimal perturbations that achieve the best balance between
transient linear amplification and flow stabilisation are determined. In the
mixing layer with b<1.5, these combined optimal perturbations appear similar to
transient growth-only optimal perturbations, and achieve a more efficient
overall stabilisation than optimal 1D and 2D modifications computed for
stabilisation only. This is consistent with the efficiency of streak-based
control strategies.Comment: 23 pages, 15 figure
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