Migration of a droplet in a cylindrical tube in the creeping flow regime

2017 ◽  
Vol 95 (3) ◽  
Author(s):  
Binita Nath ◽  
Gautam Biswas ◽  
Amaresh Dalal ◽  
Kirti Chandra Sahu
Keyword(s):  
Flow Regime ◽  
Cylindrical Tube ◽  
Creeping Flow

Process characteristics of screw impellers with a draught tube for Newtonian liquids. Time of homogenization

1981 ◽  
Vol 46 (9) ◽  
pp. 2032-2042 ◽  
Author(s):  
Pavel Seichter
Keyword(s):  
Flow Regime ◽  
Creeping Flow ◽  
Energy Requirements ◽  
Dimensionless Time ◽  
Mixing Times ◽  
Conductivity Method ◽  
Draught Tube ◽  
Process Characteristics ◽  
Newtonian Liquids

A conductivity method has been used to assess the homogenization efficiency of screw impellers with draught tubes. The value of the criterion of homochronousness, i.e. the dimensionless time of homogenization, in the creeping flow regime of Newtonian liquids is dependent on the geometrical simplexes of the mixing system. In particular, on the ratio of diameters of the vessel and the impeller and on the ratio of the screw lead to the impeller diameter. Expression have been proposed to calculate the mixing times. Efficiency has been examined of individual configurations of screw impellers. The lowest energy requirements for homogenization have been found for the system with the ratio D/d = 2.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

scholarly journals A Beale-Kato-Madja breakdown criterion for an Oldroyd-B fluid in the creeping flow regime

2008 ◽  
Vol 6 (1) ◽  
pp. 235-256 ◽  
Author(s):  
Raz Kupferman ◽  
Claude Mangoubi ◽  
Edriss S. Titi
Keyword(s):  
Flow Regime ◽  
Creeping Flow

Viscous flow in a cylindrical tube containing a line of spherical particles

1969 ◽  
Vol 38 (1) ◽  
pp. 75-96 ◽  
Author(s):  
Henry Wang ◽  
Richard Skalak
Keyword(s):  
Pressure Drop ◽  
Cylindrical Tube ◽  
Tube Diameter ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Sphere Diameter ◽  
Wide Range ◽  
Mean Pressure ◽  
Order Of Magnitude ◽  
Flow Through

The viscous, creeping flow through a cylindrical tube of a liquid, which contains rigid, spherical particles, is investigated analytically. The spheres are located on the axis of the cylinder and are equally spaced. Solutions are derived for particles in motion and fixed, with and without fluid discharge. Numerical results are presented for the drag on each sphere and the mean pressure drop for a wide range of sizes and spacings of the spheres. The study is motivated by possible application to blood flow in capillaries, where red blood cells represent particles of the same order of magnitude as the diameter of the capillary itself. The results may also be of interest in other applications, such as sedimentation and fluidized beds. It is shown that there is little interaction between particles if the spacing is more than one tube diameter, and that the additional pressure drop over that for Poiseuille flow is less than 50% if the sphere diameter is less than 0·8 of the tube diameter.

The buoyancy-driven motion of a train of viscous drops within a cylindrical tube

1992 ◽  
Vol 237 ◽  
pp. 627-648 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Cylindrical Tube ◽  
Terminal Velocity ◽  
Bond Number ◽  
Boundary Integral ◽  
Effective Radius ◽  
Creeping Flow ◽  
Boundary Integral Method ◽  
Main Body ◽  
Viscous Drops ◽  
Asymptotic Analyses

The buoyancy-driven motion of a train of viscous drops settling or rising along the axis of a vertical cylindrical tube is investigated. Under the assumption of creeping flow, the evolution of the drops is computed numerically using a boundary integral method that employs the axisymmetric periodic Green's function for flow in a cylindrical tube. Given the drop volume and assuming that the viscosity of the drops is equal to that of the suspending fluid, the motion is studied as a function of the radius of the tube, the separation between the drops, and the Bond number. Two classes of drops are considered: compact drops whose effective radius is smaller than the radius of the tube, and elongated drops whose effective radius is larger than the radius of the tube. It is found that compact drops may have a variety of steady shapes including prolate and oblate, dimpled tops, and shapes containing pockets of entrained ambient fluid. When the surface tension is sufficiently small, compact drops become unstable, evolving to prolate rings with elongated tails. The terminal velocity of compact drops is discussed and compared with that predicted by previous asymptotic analyses for spherical drops. Steady elongated drops assume the shape of long axisymmetric fingers consisting of a nearly cylindrical main body and two curved ends. Relationships between the terminal velocity of elongated drops, the gap between the drops and the wall of the tube, and the Bond number are established. The results are discussed with reference to previous analyses and laboratory measurements for inviscid bubbles.

Longitudinal Dispersion of Tracer Particles in the Blood Flowing in a Pulmonary Alveolar Sheet

1975 ◽  
Vol 42 (3) ◽  
pp. 536-540 ◽  
Author(s):  
Y. C. Fung ◽  
H. T. Tang
Keyword(s):  
Blood Flow ◽  
Cylindrical Tube ◽  
Creeping Flow ◽  
Longitudinal Dispersion ◽  
Porous Layers ◽  
Tracer Particles ◽  
The Mean ◽  
Circular Cylindrical Tube

The analysis of G. I. Taylor on the dispersion of solutes in a circular cylindrical tube is extended to the case of flow in a channel bounded by porous layers. Creeping flow in the channel and the porous layers stimulates the blood flow in the alveolar sheets of the lung. Overall perturbation on the longitudinal dispersion due to the porous layers is evaluated. It is shown that the mean coefficient of apparent diffusivity is smaller in a channel bounded by porous layers than that in a channel with impermeable walls for the case that the channel walls are permeable to solvent but not to tracer. For the case that channel walls are permeable to both solvent and tracer, the mean coefficient of apparent diffusivity is nearly the same as that of a channel with impermeable walls.

Revisiting the linear stability analysis and absolute–convective transition of two fluid core annular flow

2019 ◽  
Vol 865 ◽  
pp. 743-761 ◽  
Author(s):  
D. Salin ◽  
L. Talon
Keyword(s):  
Linear Stability ◽  
Explicit Solution ◽  
Cylindrical Tube ◽  
Flow Equation ◽  
Immiscible Fluids ◽  
Creeping Flow ◽  
Complex Eigenvalue ◽  
Miscible Fluids ◽  
Two Fluids ◽  
Fluid Core

Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

scholarly journals A chaotic serpentine mixer efficient in the creeping flow regime: from design concept to optimization

2009 ◽  
Vol 7 (6) ◽  
Author(s):  
Tae Gon Kang ◽  
Mrityunjay K. Singh ◽  
Patrick D. Anderson ◽  
Han E. H. Meijer
Keyword(s):  
Flow Regime ◽  
Creeping Flow ◽  
Design Concept
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