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

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

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

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, $Ca$, from $10^{-4}$ to $1$ and inner-to-outer viscosity ratios, $\lambda$, from $0$, 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 $Ca$. With these models at hand, we can compute the pressure drop induced by the droplet. The film thickness at low capillary numbers ($Ca<10^{-3}$) agrees well with Bretherton's scaling for bubbles as long as $\lambda<1$. For larger viscosity ratios, the film thickness increases monotonically, before saturating for $\lambda>10^3$ to a value $2^{2/3}$ 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 $Ca>10^{-3}$

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