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The '''tubular pinch effect''' is a phenomenon in [[fluid mechanics]], which has importance in [[membrane technology]].  
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Mark C. Porter first suspected that the pinch effect was responsible for the return of separated particles into the core flow by the membrane. This effect was first demonstrated in 1956 by G. Sergé and A. Silberberg. They had been working with dilute suspensions of spherical particles in pipelines. While the particle was flowing through the pipeline, it appeared to migrate away from the pipe axis and pipe wall and reach equilibrium in a radial eccentric position.  
[[File:Pinch-Effekt (Rohr) DE.svg | thumb | Radial distribution of the particle concentration c in a tube during the flow-through]]
 
If:
{|Class="wikitable"
|-
|<math>v_p</math> ||radial velocity component of a particle
|-
|<math>d_T</math> ||tube diameter
|-
|<math>d_p</math> ||particle diameter
|-
|<math>r^*</math> ||equilibrium radius
|-
|<math>w^*</math> ||mean flow velocity
|-
|<math>Re</math> ||[[Reynolds number]]
|-
|<math>r</math> ||radius
|}
 
then the pinch effect follows the relaton:
 
:<math>v_\text{p}=0{,}17 \cdot w^* \cdot Re \cdot {\left( \frac{d_\text{p}}{d_\text{T}} \right)} ^{2{,}84} \cdot \frac{2r}{d_\text{T}}\cdot \left(1 - \frac{r}{r^*}\right)</math>
 
This effect is of importance in [[cross-flow filtration]] and especially in [[dialysis]]. It is significant especially for particles with a diameter of 5&nbsp;[[µm]] and for particles which follow [[laminar flow]] conditions and slows down the process of [[filter cake]] formation, which prolongs the service life and the filtering stays permanently high.
 
== References ==
* Munir Cheryan ''Handbuch Ultrafiltration'' B. Behr's Verlag GmbH&Co ISBN 3-925673-87-3 (1990)
* Meyers Lexikon online 2.0
* Siegfried Ripperger, ''Berechnungsansätze zur Crossflow-Filtration'', Chemieingenieurtechnik, (1993) p.533-540 doi:10.1002/cite.330650506
* G. Segré, A. Silberberg, ''Behaviour of Macroscopic Rigid Spheres in Poiseuille Flow. Part 1. Determination of Local Concentration by Statistical Analysis of Particle Passages Through Crossed Light Beams'', Journal of Fluid Mechanics Digital Archive, (1962) p. 115-135
* G. Segré, A. Silberberg ''Behaviour of Macroscopic Rigid Spheres in Poiseuille Flow. Part 2. Experimental Results and Interpretation'', Journal of Fluid Mechanics Digital Archive, (1962) p.136-157
 
[[Category:Fluid mechanics]]
[[Category:Piping]]
[[Category:Membrane technology]]

Latest revision as of 17:21, 27 December 2014

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