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.

Process characteristics of screw impellers with a draught tube for Newtonian liquids. Pumping capacity of the impeller

1981 ◽  
Vol 46 (9) ◽  
pp. 2021-2031 ◽  
Author(s):  
Pavel Seichter
Keyword(s):  
Viscous Liquid ◽  
Energy Criterion ◽  
Velocity Profiles ◽  
Newtonian Liquid ◽  
Creeping Flow ◽  
Geometrical Arrangement ◽  
Draught Tube ◽  
Process Characteristics ◽  
Newtonian Liquids

Velocity profiles and pumping capacity have been determined using a thermistor anemometer in a vessel equipped with a screw impeller. In region of the creeping flow of a Newtonian liquid, i.e. for Re <15, the dimensionless pumping capacity is dependent on the geometrical arrangement of the mixing system. The efficiency was assessed of individual configuration from the value energy criterion expressing the dimensionless power requirements for recirculation of a highly viscous liquid in a vessel equipped with a screw impeller.

Process characteristics of screw impellers with a draught tube for Newtonian liquids. The power input

1981 ◽  
Vol 46 (9) ◽  
pp. 2007-2020 ◽  
Author(s):  
Pavel Seichter ◽  
Jiří Dohnal ◽  
František Rieger
Keyword(s):  
Reynolds Number ◽  
Experimental Verification ◽  
Power Input ◽  
Creeping Flow ◽  
Total Power ◽  
Geometrical Parameters ◽  
Draught Tube ◽  
Process Characteristics ◽  
Wide Range ◽  
Newtonian Liquids

An expression has been proposed for the power input of a screw impeller with a draught tube in the creeping flow regime based on the analogy with extruder screws. Experimental verification has confirmed practical utility of the expression in a wide range of geometrical parameters of the impeller and for the Reynolds number for mixing below 20. The total power input of the impeller is expressed as a sum of the input inducing the drag flow and the input to create the pressure flow. The former of the inputs may be deduced from the theory of extruders while an empirical approach based on experiment has been used to formulate an expression for the latter.

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

Generation and breakup of Worthington jets after cavity collapse. Part 2. Tip breakup of stretched jets

2010 ◽  
Vol 663 ◽  
pp. 331-346 ◽  
Author(s):  
J. M. GORDILLO ◽  
STEPHAN GEKLE
Keyword(s):  
High Speed ◽  
Local Strain ◽  
External Noise ◽  
Creeping Flow ◽  
Liquid Density ◽  
Dimensionless Time ◽  
Cavity Collapse ◽  
Flow Limit ◽  
Theoretical Predictions ◽  
High Reynolds

The capillary breakup of the high-speed Worthington jets ejected after a cavity collapse in water occurs due to the high-Reynolds-number version of the capillary end-pinching mechanism first described, in the creeping flow limit, by Stone & Leal (J. Fluid Mech., vol. 198, 1989, p. 399). Using potential flow numerical simulations and theory, we find that the resulting drop ejection process does not depend on external noise and can be described as a function of a single dimensionless parameter, WeS = ρ R30S20/σ, which expresses the ratio of the capillary time to the inverse of the local strain rate, S0. Here, ρ and σ indicate the liquid density and the interfacial tension coefficient, respectively, and R0 is the initial radius of the jet. Our physical arguments predict the dimensionless size of the drops to scale as Ddrop/R0 ~ We−1/7S and the dimensionless time to break up as TS0 ~ We2/7S. These theoretical predictions are in good agreement with the numerical results.

scholarly journals Kinetics of Spreading over Porous Substrates

2019 ◽  
Vol 3 (1) ◽  
pp. 38 ◽  
Author(s):  
Phillip Johnson ◽  
Anna Trybala ◽  
Victor Starov
Keyword(s):  
Contact Angle ◽  
Porous Layer ◽  
Filter Paper ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dimensionless Time ◽  
Complete Wetting ◽  
Porous Layers ◽  
Newtonian Liquids ◽  
Porous Substrates

The spreading of small liquid drops over thin and thick porous layers (dry or saturated with the same liquid) is discussed in the case of both complete wetting (silicone oils of different viscosities over nitrocellulose membranes and blood over a filter paper) and partial wetting (aqueous SDS (Sodium dodecyl sulfate) solutions of different concentrations and blood over partially wetted substrates). Filter paper and nitrocellulose membranes of different porosity and different average pore size were used as a model of thin porous layers, sponges, glass and metal filters were used as a model of thick porous substrates. Spreading of both Newtonian and non-Newtonian liquid are considered below. In the case of complete wetting, two spreading regimes were found (i) the fast spreading regime, when imbibition is not important and (ii) the second slow regime when imbibition dominates. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations was derived in the case of complete wetting for both Newtonian and non-Newtonian liquids to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. The deduced system of differential equations does not include any fitting parameter. Experiments were carried out by the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions) and blood over dry filter paper. The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactorily for the experimental data. According to the theory prediction, (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation in the case of complete wetting. These conclusions again are in good agreement with experimental observations in the case of complete wetting for both Newtonian and non-Newtonian liquids. Addition of surfactant to aqueous solutions, as expected, improve spreading over porous substrates and, in some cases, results in switching from partial to complete wetting. It was shown that for the spreading of surfactant solutions on thick porous substrates there is a minimum contact angle after which the droplet rapidly absorbs into the substrate. Unfortunately, a theory of spreading/imbibition over thick porous substrates is still to be developed. However, it was shown that the dimensionless time dependences of both contact angle and spreading radius of the droplet on thick porous material fall on to a universal curve in the case of complete wetting.

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

Numerical Study on Mixing in a Chaotic Serpentine Mixer Using a Mapping Method

2009 ◽  
Author(s):  
T. G. Kang ◽  
M. K. Singh ◽  
P. D. Anderson ◽  
H. E. H. Meijer
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Stokes Flow ◽  
Mapping Method ◽  
Creeping Flow ◽  
Chaotic Mixing ◽  
Original Design ◽  
Two Fluids ◽  
Serpentine Channel ◽  
Design Variables

We introduce a chaotic serpentine mixer (CSM), which is motivated by the three-dimensional serpentine channel [Liu et al., 2000, J. Microelectromech. Syst. 9, pp. 190–197], and demonstrate a systematic way of utilizing the mapping method [Singh et al., 2008, Microfluid Nanofluid 5, pp. 313–325] to find out an optimal set of design variables for the new mixer. The new mixer shows globally chaotic mixing even in the Stokes flow regime, while maintaining the benefits of the original design. One geometrical period of the mixer consists of two functional units, inducing two flow portraits with crossing streamlines. Each half period of the mixer consists of an “L-shaped” bend and a bypass channel. The two flow portraits may be either co-rotational or counter-rotational. As a preliminary study, first of all, mixing in the original serpentine channel has been analyzed to demonstrate the flow characteristics and to find out a critical Reynolds number showing chaotic mixing above the limit. The working principle of the newly proposed mixer is explained by the manifold of the deforming interface between two fluids. To optimize the mixer, we choose three key design variables: the sense of rotation of the two flows, the aspect ratio of the rectangular channel, and the lateral location of the bypass channel. Then, simulations for all possible combinations of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the creeping flow regime. The design windows, provided as a result of the parameter study, can be used to determine a proper set of the design variables to fit with a specific application. The deforming interface of the two fluids shows that, even in a poor mixer in Stokes flow regime, as the Reynolds number increases, more efficient mixing is resulted in due to the enhanced cross-sectional vertical motion and back flows near the bends.

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
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