Pinch effect (fluid mechanics)

As pinch effect (engl .: to pinch , dt., 'Pinch) is a phenomenon of the fluid mechanics referred to, which, inter alia, the membrane technology is important.

Mark C. Porter was the first to suspect that the so-called pinch effect (including tubular pinch effect) is responsible for the return transport of separated particles from the membrane into the core flow. In 1956, G. Segré and A. Silberberg demonstrated this effect for the first time while working with dilute suspensions of spherical particles in pipelines. When flowing through the same, the particles apparently migrated away from the pipe wall and pipe axis and reached an equilibrium in an eccentric radial position.

Radial distribution of the particle concentration c in a pipe with a flow

If

${\ displaystyle v_ {p}}$	radial velocity component of a particle
${\ displaystyle d_ {T}}$	Pipe diameter
${\ displaystyle d_ {p}}$	Particle diameter
${\ displaystyle r ^ {*}}$	Equilibrium radius
${\ displaystyle w ^ {*}}$	mean flow velocity
${\ displaystyle Re}$	Reynolds number
${\ displaystyle r}$	radius

then the pinch effect is based on the following relationship:

{\ displaystyle 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)}

This effect is important in membrane technology in tangential flow filtration and especially in dialysis . It is particularly important for particles with a diameter of 5 µm and above and laminar flow conditions and slows down the process of filter cake formation , which extends the service life and keeps the filtration performance high in the long term.

literature

Munir Cheryan: Handbook of Ultrafiltration . B. Behr's Verlag GmbH & Co, 1990, ISBN 3-925673-87-3 .
Meyer's Lexicon online 2.0
Siegfried Ripperger: Calculation Approaches for Crossflow Filtration . In: Chemical engineering . tape 65 , no. 5 , 1993, p. 533-540 , doi : 10.1002 / cite.330650506 .
G. Segré, A. Silberberg: Behavior of Macroscopic Rigid Spheres in Poiseuille Flow. Part 1. Determination of Local Concentration by Statistical Analysis of Particle Passages Through Crossed Light Beams . In: Journal of Fluid Mechanics Digital Archive . tape 14 , 1962, pp. 115-135 .
G. Segré, A. Silberberg: Behavior of Macroscopic Rigid Spheres in Poiseuille Flow. Part 2. Experimental Results and Interpretation . In: Journal of Fluid Mechanics Digital Archive . tape 14 , 1962, pp. 136-157 .