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.

Passive micromixers for applications in the microreactor and μTAS fields

Abstract: An overview is given of current developments in micromixing technology, where the emphasis is on liquid mixing in passive micromixers. The mixers presented are differentiated by the hydrodynamic principle employed, and four important principles are discussed in some detail: hydrodynamic focusing, flow separation, chaotic advection, and split-and-recombine flows. It is shown that these principles offer excellent mixing performance in various dynamical regimes. Hydrodynamic focusing is a concept working very much independently of the Reynolds number of the flow. Flow separation offers rich dynamical behavior over a Reynolds number scale of several hundred, with superior performance compared to purely diffusive mixing already found at low Reynolds numbers. For chaotic advection, different implementations tailor-made for low and comparatively high Reynolds numbers exist, both leading to an exponential increase of the interface between two fluids. Split-and-recombine flows can only be realized in a close-to-ideal form in the low Reynolds number regime. Corresponding mixers can be equipped with comparatively wide channels, enabling a favorable ratio of throughput to pressure drop. The overview given in this article should enable a potential user of micromixing technology to select the most favorable concept for the application envisaged, especially in the field of chemical process technology

Non-Newtonian Fluid Mechanics

Abstract: 1. Principles of Continuum Mechanics. Basic Concepts. Material Derivative. Deformation Rates. Rivlin-Ericksen Tensors. Strain Tensor. Kinematics of Steady Shear Flows. Continuity Equation. Stress and Volume Force. Equations of Motion. Energy Equation for Fluid Flow. 2. Material Properties Occurring in Steady Shear Flows. The Flow Function. The Normal Stress Functions. 3. Processes that are Controlled by the Flow Function. Rotational Viscometer. Pressure-Drag Flow in a Straight Channel. Radial Flow between Two Parallel Planes. Pipe Flow. Helical Flow. 4. Effect of Normal Stress Differences. Cone-and-Plate Flow. Weissenberg Effect. Die-Swell. Axial Shear Flow. 5. Simple Unsteady Flows. Linear Viscoelasticity. Non-Linear Effects in Unsteady Pipe Flow. 6. Nearly Viscometric Flows. Shear Flows with a Weak Unsteady Component. Plane Steady Boundary Layer Flows. Stability of Plane Shear Flows. 7. Extensional Flows. Theoretical Principles. Applications. 8. Special Rheological Laws. Fluids Without Memory. Integral Models. Differential Models. Approximation for Slow and Slowly Varying Processes. 9. Secondary Flows. General Theory. Rotational Symmetric Flows. Plane Flows. Steady Flow through Cylindrical Pipes. Periodic Pipe Flow. Appendix: Set of Formulas for Special Curvilinear Coordinates. References. Index.

Numerical Solution of a Uniform Flow over a Sphere at Intermediate Reynolds Numbers

Abstract: Numerical solutions of the transient uniform flow around a sphere are obtained. The transition takes place between an initial potential flow and a fully developed viscous field. The fluid is incompressible, homogeneous, and its flow is governed by the complete Navier‐Stokes equations. The range of Reynolds number studied is Re = 1–1000 where a recirculatory wake appears and the nonlinear terms are essential, that is, they cannot be neglected or approximated. The flow is assumed to be axisymmetric throughout this range. A time‐dependent stream function‐vorticity formulation is adopted. The solution is obtained by constructing a finite difference approximation to the vorticity transport equation on an expanding spherical polar grid system. Central differencing of second‐order accuracy both in time (Dufort‐Frankel) and space is utilized. Experiments with numerical stability show an appreciable deviation from linearized stability analysis due to the large gradients of vorticity in the field. Quantitative physical results are obtained. The geometrical parameters characterizing the recirculatory wake compare favorably with those recorded in physical experiments. The detailed distribution of the vorticity on the sphere agrees with results obtained via the steady‐state approach at Re = 10, 40, and 100. The computed drag coefficient CD agrees well with the standard drag curve over the range of Reynolds numbers investigated.

Finite element simulation of an electroosmotic-driven flow division at a T-junction of microscale dimensions

Abstract: A finite element formulation is developed for the simulation of an electroosmotic flow in rectangular microscale channel networks. The distribution of the flow at a decoupling T-junction is investigated from a hydrodynamic standpoint in the case of a pressure-driven and an electroosmotically driven flow. The calculations are carried out in two steps: first solving the potential distribution arising from the external electric field and from the inherent zeta potential. These distributions are then injected in the Navier Stokes equation for the calculation of the velocity profile. The influence of the various parameters such as the zeta potential distribution, the Reynolds number, and the relative channel widths on the flow distribution is investigated.