Next Article in Journal
Preparation and Characterization of Thermoresponsive Poly(N-isopropylacrylamide-co-acrylic acid)-Grafted Hollow Fe3O4/SiO2 Microspheres with Surface Holes for BSA Release
Previous Article in Journal
Fracture Analysis of MWCNT/Epoxy Nanocomposite Film Deposited on Aluminum Substrate
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle
Materials 2017, 10(4), 409;

Tortuosity of Aligned Channels in Alumina Membranes Produced by Vacuum-Induced Surface Directional Freezing

Division of Pharmaceutics, University of Erlangen, 91054 Erlangen, Germany
Department of Material Science and Engineering, University of Erlangen, 91054 Erlangen, Germany
Author to whom correspondence should be addressed.
Academic Editor: Marco Salerno
Received: 5 February 2017 / Revised: 16 March 2017 / Accepted: 30 March 2017 / Published: 14 April 2017
Full-Text   |   PDF [4145 KB, uploaded 14 April 2017]   |  


Vacuum-induced surface freezing of colloidal alumina was used to produce membranes that have elongated, aligned channels and, hence, are tortuous in the direction perpendicular to ice crystal growth. The effective tortuosity of the membranes was measured by steady-state diffusion of a solute, methylene blue. The resulting diffusion profiles show an initial step-increase in amount of dye reaching the acceptor that is caused by capillarity drawing the donor solution through any non-wetted channels in the membrane. This is followed by a linear steady-state phase whose flux is proportional to dye concentration in the donor and inversely proportional to the colloid’s volume fraction of dispersed phase. From the steady-state flux, the effective tortuosity, τ* = (α/τ)−1, was calculated. This is the reciprocal quotient of the reduced available area for diffusion within the membrane, α = A*/A, where A* is the available area and A is the cross-sectional area of the membrane, and the increased mean diffusional path length, i.e., tortuosity = L * / L , where L* is the mean path length and L is the membrane thickness. The values of τ* lie in the range of 2–38 and increase as the volume fraction of dispersed phase is larger. This latter effect indicates that τ* > 1 results, to a larger extent, from the reduced available diffusion area, α, than from the lengthened pathway, τ, in these aligned porous membranes. View Full-Text
Keywords: alumina; directional freezing; tortuosity alumina; directional freezing; tortuosity

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Großberger, S.; Fey, T.; Lee, G. Tortuosity of Aligned Channels in Alumina Membranes Produced by Vacuum-Induced Surface Directional Freezing. Materials 2017, 10, 409.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Materials EISSN 1996-1944 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top