摘要:

The pressure‐driven flow of a periodic suspension of two‐dimensional viscous drops in a channel that is bounded by two parallel plane walls is studied numerically using the method of interfacial dynamics, which is an improved version of the boundary integral method. The viscosity of the drops is assumed to be equal to that of the suspending fluid. The effects of capillary number, volume fraction, and number of rows are examined for ordered suspensions, where the drops are initially arranged in several rows on a hexagonal lattice. Results of dynamic simulations for random monodisperse suspensions with up to 12 drops per periodic cell are performed, and the salient features of the motion are discussed. It is found that, in all cases, the drops tend to migrate toward the centerline of the channel, forming either a single row or multiple rows. The effect of the instantaneous suspension microstructure on the effective viscosity is illustrated, and some important differences in the behavior of suspensions in pressure‐driven and shear‐driven flows are identified and discussed. Numerical evidence is presented, suggesting that the behavior of suspensions of high viscosity drops may be significantly different from that of suspensions of drops with small and moderate viscosity.

ISSN:1070-6631    

DOI:10.1063/1.868048

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The nonlinear evolution of viscous fingering instabilities in miscible displacement flows in porous media with nonmonotonic viscosity profiles is investigated. The flow is accurately simulated using a Hartley transform based spectral method. A flow with nonmonotonic viscosity profile has an unstable region followed downstream by a stable region. Instabilities first begin in the unstable region and then grow and penetrate the stable region. The striking contrast between viscous fingering in flows with monotonic and nonmonotonic viscosity profiles is the direction of fluid penetration. The nonmonotonicity in the viscosity profile gives rise to a new phenomena of ‘‘reverse’’ fingering in which the displaced fluid fingers through the displacing fluid more readily than vice versa. A forward and a reverse mixing lengths are defined to characterize the growth of the mixing zone in the two directions. At large times, both the forward and reverse mixing lengths grow linearly in time. A model nonmonotonic viscosity profile is used to parametrically study the asymptotic mixing rates. The parametric study shows that for a given end point and maximum viscosities the growth rate of the mixing zone varies nonmonotonically with the length of the stable barrier in the viscosity profile. A physical mechanism is put forth to explain the observed phenomena of reverse fingering and its dependence on the parameters of the problem. Finally, a finger is isolated and its evolution is studied to understand the differences in the mechanisms that control the growth of a finger in flows with monotonic and nonmonotonic viscosity profiles.

ISSN:1070-6631    

DOI:10.1063/1.868049

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The dispersion of a passive tracer in fluid flowing between a source and a sink in a Hele–Shaw geometry, characteristic of field scale flows in a layer or fracture, is considered. A combination of analytic and numerical techniques and complementary experimental measurements are employed, leading to a consistent picture. This dispersion process is found to be characterized by a power‐law decay in time of the tracer concentration, with an exponential cutoff at very long times, in strong contrast to the Gaussian behavior associated with the widely used quasi‐one‐dimensional (1‐D) models.

ISSN:1070-6631    

DOI:10.1063/1.868075

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Modons correspond to isolated dipole vortex solutions of the quasigeostrophic equations. They have been proposed as prototype models for some geophysical (and plasma) vortices. The classical modon solution on a &bgr; plane does not permit a Rossby wave field in the exterior or far‐field region of the modon. However, it is qualitatively known that the gravest mode associated with a normal mode decomposition of a stationary modon in a continuously stratified fluid of finite depth necessarily contains a Rossby wave tail in the downstream region if the background flow is eastward. The same effect can be formally recreated in an equivalent‐barotropic model of a stationary modon embedded in a constant eastward zonal flow. An analytical solution to this problem satisfying the correct upstream radiation condition is presented and its dynamical characteristics are discussed.

ISSN:1070-6631    

DOI:10.1063/1.868427

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A low‐dimensional Galerkin method for the three‐dimensional flow around a circular cylinder is constructed. The investigation of the wake solutions for a variety of basic modes, Hilbert spaces, and expansion modes reveals general mathematical and physical aspects which may strongly effect the success of low‐dimensional simulations. Besides the cylinder wake, detailed information about the construction of similar low‐dimensional Galerkin methods for the sphere wake, the boundary‐layer, the flow in a channel or pipe, the Taylor–Couette problem, and a variety of other flows is given.

ISSN:1070-6631    

DOI:10.1063/1.868433

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A linear stability analysis has been carried out for flow between porous concentric cylinders when radial flow is present. Several radius ratios with corotating and counter‐rotating cylinders were considered. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius, was varied from −30 to 30. The stability equations form an eigenvalue problem that was solved using a numerical technique based on the Runge–Kutta method combined with a shooting procedure. The results reveal that the critical Taylor number at which Taylor vortices first appear decreases and then increases as the radial Reynolds number becomes more positive. The critical Taylor number increases as the radial Reynolds number becomes more negative. Thus, radially inward flow and strong outward flow have a stabilizing effect, while weak outward flow has a destabilizing effect on the Taylor vortex instability. Profiles of the relative amplitude of the perturbed velocities show that radially inward flow shifts the Taylor vortices toward the inner cylinder, while radially outward flow shifts the Taylor vortices toward the outer cylinder. The shift increases with the magnitude of the radial Reynolds number and as the annular gap widens.

ISSN:1070-6631    

DOI:10.1063/1.868077

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

The stability of the large Reynolds number flow of a Newtonian fluid over a much more viscous viscoelastic fluid is studied via a linear analysis. The two fluids are confined within a channel and the flow is driven by the motion of the plate bounding the Newtonian fluid. Matched asymptotic expansions are used to derive the dispersion relation, and the flow is found to be always unstable to an interfacial mode due to the discontinuity in the fluid viscosities. It is shown that even a small amount of elasticity of the viscoelastic fluid can change the stability characteristics considerably.  

ISSN:1070-6631    

DOI:10.1063/1.868078

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

In this paper the conditions under which the Kelvin–Helmholtz instability in stratified fluids is absolute or convective are investigated. It is first shown that at transition from convective to absolute instability two double roots of the dispersion relation coalesce. Based on this property an analytical condition for absolute instability is derived. It is found that the instability is absolute for almost all values of the flow velocity and stratification. Convective instability is found only for a narrow range of flow velocities over the instability threshold when the density ratio parameter,r=&rgr;1/(&rgr;1+&rgr;2), lies in the range 1/3<r<1/2. The different behavior near the instability threshold can be related to the signs of the group velocities of the two waves which coalesce to create the instability: Forr<1/3, the group velocities of the two waves have opposite signs, and the resulting instability is absolute, whereas for 1/3<r<1/2, the two waves have group velocities with the same sign, and the instability is convective. This result is also shown to be reflected in the form of the amplitude equation at the instability threshold, which is the linearly unstable Klein–Gordon equation.

ISSN:1070-6631    

DOI:10.1063/1.868079

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

Local analysis of the onset of instability in flows that are not exactly parallel is considered. Corrections to the Orr–Sommerfeld equation arising as a consequence of the nonparallelism of the unperturbed flow are studied. The quasiparallel hypothesis is quantified on a model of Gaussian plane wave packets. It appears that the characteristic length scales of the downstream dependence of flow field characteristics must be substantially larger than the inverse of the wave number characterizing the instability. A new eigenvalue problem describing the propagation of these Gaussian wave packets is written. The relation between the marginal and absolute instability analysis for marginal Reynolds numbers is discussed. For flows varying slowly in the downstream direction, closed‐form corrections of the Orr–Sommerfeld equation terms taking account of thexvariation of the flow field and of the extension of the propagating wave packets are derived. A first‐order perturbation theory correction of the Orr–Sommerfeld dispersion relation is proposed, allowing the reduction of the calculation of nonparallel corrections of the local instability quantities to quadratures. The proposed theory is applied to two important cases: the Blasius boundary layer and the cylinder wake. For the Blasius boundary layer the basic condition of applicability of the quasiparallel theory is found to be satisfied. However, the nonparallel correction of the critical Reynolds number is found to be non‐negligible and provides a good agreement with experimental results. In the cylinder wake case direct bidimensional simulation results are used to assess the downstream variation of the flow field characteristics. The characteristic length scale of this variation in the near wake is found to be of the order of unity, which is also the magnitude of the wave numbers characterizing the local absolute instabilities in this region. Hence, the Orr–Sommerfeld analysis and any corrections based on the propagation of plane waves in the wake can hardly be expected to provide more than qualitative results.

ISSN:1070-6631    

DOI:10.1063/1.868080

出版商:AIP    

年代:1994

数据来源: AIP

摘要:

A dissipation‐modified Boussinesq‐like system of equations governing three‐dimensional long wavelength Marangoni–Be´nard oscillatory convection in a shallow layer heated from the air side is presented. Solitary waves and their oblique and head‐on interactions are considered, thus leading to results that compare well with available experimental data.

ISSN:1070-6631    

DOI:10.1063/1.868081

出版商:AIP    

年代:1994

数据来源: AIP