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Modelling of optimal back-shock frequency in hollow-fibre ultrafiltration membranes II : Semi-analytical mathematical model

Vinther, Frank LU and Jönsson, Ann Sofi LU (2016) In Journal of Membrane Science 506. p.137-143
Abstract

The influence of cross-flow velocity and transmembrane pressure on the optimal back-shock frequency and normalized net flux during back-shocking has been studied using a semi-analytical mathematical model. The model uses the flux as a function of time without back-shocking together with knowledge of the streamlines and pathlines during the back-shock cycle to predict the optimal normalized net flux as a function of forward filtration time. The model was used to investigate three different transmembrane pressures and three different cross-flow velocities during a back-shock cycle. The net flux was found to increase under all operating conditions when using back-shocking. The greatest increase in normalized net flux was found at the... (More)

The influence of cross-flow velocity and transmembrane pressure on the optimal back-shock frequency and normalized net flux during back-shocking has been studied using a semi-analytical mathematical model. The model uses the flux as a function of time without back-shocking together with knowledge of the streamlines and pathlines during the back-shock cycle to predict the optimal normalized net flux as a function of forward filtration time. The model was used to investigate three different transmembrane pressures and three different cross-flow velocities during a back-shock cycle. The net flux was found to increase under all operating conditions when using back-shocking. The greatest increase in normalized net flux was found at the highest cross-flow velocity and the highest transmembrane pressure, and corresponds to an increase of 37% compared to the steady-state flux. The highest cross-flow velocity and the highest transmembrane pressure gave the highest optimal back-shock frequency of 0.21 Hz. The optimal back-shock frequency was found to decrease with increasing pressure and decreasing cross-flow velocity.The model is easy to use in different applications as it is easy to measure flux during forward filtration without back-shocking. Good agreement was found between the semi-analytical model and a model based on computer fluid dynamics in predicting both the value of the optimal normalized net flux and the optimal back-shock frequency.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Back-shock frequency, Back-shocking, Mathematical modelling, Net flux, Semi-analytical model, Ultrafiltration
in
Journal of Membrane Science
volume
506
pages
7 pages
publisher
Elsevier
external identifiers
  • Scopus:84959095611
  • WOS:000370875900014
  • Scopus:84968442917
ISSN
0376-7388
DOI
10.1016/j.memsci.2016.01.040
language
English
LU publication?
yes
id
1d8256d1-74c4-4974-8484-50b4d116caa6
date added to LUP
2016-05-10 08:36:05
date last changed
2017-01-01 08:25:38
@article{1d8256d1-74c4-4974-8484-50b4d116caa6,
  abstract     = {<p>The influence of cross-flow velocity and transmembrane pressure on the optimal back-shock frequency and normalized net flux during back-shocking has been studied using a semi-analytical mathematical model. The model uses the flux as a function of time without back-shocking together with knowledge of the streamlines and pathlines during the back-shock cycle to predict the optimal normalized net flux as a function of forward filtration time. The model was used to investigate three different transmembrane pressures and three different cross-flow velocities during a back-shock cycle. The net flux was found to increase under all operating conditions when using back-shocking. The greatest increase in normalized net flux was found at the highest cross-flow velocity and the highest transmembrane pressure, and corresponds to an increase of 37% compared to the steady-state flux. The highest cross-flow velocity and the highest transmembrane pressure gave the highest optimal back-shock frequency of 0.21 Hz. The optimal back-shock frequency was found to decrease with increasing pressure and decreasing cross-flow velocity.The model is easy to use in different applications as it is easy to measure flux during forward filtration without back-shocking. Good agreement was found between the semi-analytical model and a model based on computer fluid dynamics in predicting both the value of the optimal normalized net flux and the optimal back-shock frequency.</p>},
  author       = {Vinther, Frank and Jönsson, Ann Sofi},
  issn         = {0376-7388},
  keyword      = {Back-shock frequency,Back-shocking,Mathematical modelling,Net flux,Semi-analytical model,Ultrafiltration},
  language     = {eng},
  month        = {05},
  pages        = {137--143},
  publisher    = {Elsevier},
  series       = {Journal of Membrane Science},
  title        = {Modelling of optimal back-shock frequency in hollow-fibre ultrafiltration membranes II : Semi-analytical mathematical model},
  url          = {http://dx.doi.org/10.1016/j.memsci.2016.01.040},
  volume       = {506},
  year         = {2016},
}