Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Stability of stratified two-phase flows in horizontal channels

Abstract: Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.

Flow regimes and mass transfer characteristics in static micromixers

Abstract: The design and calculation of micro mixers is done by conventional analytical and numerical calculations. Due to the small dimensions, laminar flow is expected and the mass transfer is supposed to be dominated by diffusion. A detailed CFD-study by CFDRC-ACE+ of simple static mixers shows a deviation from strictly laminar flow in a wide range of Re numbers and channel dimensions. The static mixers under test have a T-Profile with rectangular cross sections and characteristic dimensions of 50 to 400 μm. The mean flow velocity is varied from 0,01 m/s to 5 m/s, which are typical values for chemical and biological applications, chemical analysis, and microfluidics with acceptable pressure losses. With increasing flow velocity and increasing Re numbers the flow starts to develop a vortex at the entrance of the mixing channel. With further increasing velocity the flow tends to instabilities, which causes the break up of the flow symmetry. With the onset of the vortex formation and with the occurrence of the flow instabilities the mass transfer is enhanced by the exchange of fluid elements. The laminar diffusion model cannot describe this mixing effect. A simple analytical model for first calculations is proposed.

Separation in the flow through peristaltic motion of a carreau fluid in uniform tube

Abstract: The problem of separated flow (trapping) through peristaltic motion of an incompressible carreau fluid in uniform tube has been investigated under long wavelength approximation neglecting the wave number and using a perturbation series in the Weissenberg number ( Wi ) was used to obtain explicit forms for the velocity field, a relation between the flow rate and the pressure gradient and a relation between the friction force and the flow rate, in terms of parameter Weissenberg number ( Wi ), power-law index ( n ) and amplitude ratio φ . A condition frequently used to predict separated flow in boundary layer theory is to set the vorticity equal to zero on the boundary. We solve the problem numerically using Newton Raphson method to get separated flow points on the wall surface. From our results, the trapping region at the wall decreases with increasing volume flow rate and we found that there exist two values of longitudinal component of separated flow points one of them approaches to inlet of contraction and the other approaches to outlet of contraction. Also, the magnitude of radial velocity of the fluid at the separated flow points for Newtonian fluid is greater than non-Newtonian fluid and the magnitude of pressure rise at separated flow points approximately has the same values at the two values of the longitudinal component of separated flow points. Moreover, the friction force at separated flow points declare reflux phenomena in the contraction region. We discuss behavior of the vertical velocity, the pressure rise and the friction force at separated flow points for the physical parameters of interest.

A numerical study of the effect of surface tension and noise on an expanding Hele-Shaw bubble

Abstract: In this paper, the dynamics of an interface under the influence of surface tension is studied numerically for flow in the Hele–Shaw cell, where the interface separates an expanding bubble of inviscid fluid from a displaced viscous fluid. Of special interest is the long–time behavior of the so‐called q‐pole initial data, whose motion is explicitly known and globally smooth for the zero surface tension flow. The numerical method is spectrally accurate and based upon a boundary integral formulation of the problem, together with a special choice for the frame of motion along the interface. In 64‐bit arithmetic, a transition from the formation of side branches to tip splitting is observed as the surface tension is decreased. The tip splitting occurs on a time scale that decreases with the surface tension. This is consistent with some experimental observations. However, by increasing the arithmetic precision to 128 bits, it is found that this transition occurs at a yet smaller surface tension. The tip splitting is associated with the growth of noise in the calculation at unstable scales allowed by the surface tension, and a simple linear model of this growth seems to agree well with the observed behavior. The robustness of the various observed structures to varying amounts of noise is also investigated numerically. It is found that the appearance of side branches seems to be the intrinsic effect of surface tension, and the time scales for their appearance increases as the surface tension decreases. These results suggest, with some qualification, that surface tension acts as a regular perturbation to evolution from this initial data, even for long times.

The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake

Abstract: The Navier-Stokes equations are solved numerically for the steady separated flow past a normal flat plate for Reynolds numbers in the range 0.1 ≤ R ≤ 20. Eddy dimensions together with the position of the vortex centre are presented and compared with the few other estimates and predictions available. Streamlines and equivorticity lines are also given. The main result of interest is the extremely good comparison with experimental results over this range of Reynolds numbers. The method of solution is based on an artificial time-dependent procedure using a distorted time. Results are given only for the steady-state flow.