Solid State Nuclear Magnetic Resonance 25 (2004) 28–34 Visualizationoftransport:NMRmicroscopyexperimentswithmodel objects for porous media with pore sizes down to 50 mm Elke Kossel, Markus Weber, and Rainer Kimmich  Sektion Kernresonanzspektroskopie, Universita¨t Ulm, Albert-Einstein-Alle 11, 89069 Ulm, Germany Received November 7, 2002; revised March 21, 2003 Abstract Hydrodynamic flow and electric currents through model porous media were investigated. The transport rates through the individualpathwaysoftheporenetworkaredeterminedbythelocalwidthoftheporechannelsandbythedrivingmechanism.The model objects represent quasi two-dimensional random site percolation clusters. The calculated design was realized by milling the structureinpolystyrenesheets.Velocitymapsofstationaryflowandcurrentdensitymapsofstationarycurrentsthroughthecluster were acquired by magnetic resonance imaging methods. The findings were compared to the results of numerical simulations based on the same structure. Since the difference in the transport patterns of the different driving mechanisms are expected to be more pronouncedinsmallerporespaces,ultradeepX-raylithographyhasbeenusedforthefabricationofdownsizedmodelobjectswitha spatial resolution of better than 50 mm and an aspect ratio as large as 20. First results obtained with these objects are reported. r 2003 Elsevier Inc. All rights reserved. PACS: 78.55.Mb; 47.55.Mh; 46.65+g; 47.15x Keywords: NMR; MRI; Velocity imaging; Current density mapping; Porous media; Percolation; Micro flow 1. Introduction Transport in a porous medium is influenced by the way the pore space is built up. Loops, dead ends, alternative pathways or single-pore connections form a complex network that is in general unknown in detail. The use of percolation clusters [1] as model porous media has two major advantages: Firstly, the structure of the pore space and its geometrical and fractal properties are well known and can be controlled to some extent by the creation algorithm employed. Secondly, the generated structures can be implemented innumericalsimulationsaswellasusedastemplatesfor thefabricationofrealobjects.Thereforeitispossibleto directly compare the results of experiments and numer- ical simulations for the very same structure. Experi- mental data and simulations turned out to match encouragingly well in a series of magnetic resonance imaging (MRI) experiments, where different transport mechanisms in percolation clusters have been investi- gated [2–6]. MRI techniques are noninvasive and therefore favorable for the spatially resolved investiga- tion of transport phenomena [7]. A major characteristic of fractals is the self-similarity of the structure. Percolation clusters are also self- similar, but only on length scales smaller than the correlation length x: On small length scales the appearance of self-similarity is trivially limited by the existence of a basic cluster element. In a percolation model for porous media the size of the basic element determines the smallest pore diameter within the structure. In most cases all other pore diameters are multiples of this value. As long as interactions between the percolating medium and the walls of the pore space are negligible, the actual size of the pores is of little interest. However, for small pores these interactions significantly increase the resistance. Comparing trans- port behavior in large and small pore geometries is one interesting possibility of the work with well-character- ized pore spaces. On the other hand, the dependence of the resistance on the pore diameter differs for different driving mechanisms. The investigation of the influence of the resistance on the formation of the distinct transport pathways is another intriguing objective of this study. ARTICLE IN PRESS  Corresponding author. Fax: +49-731-502-3150. E-mail address: rainer.kimmich@physik.uni-ulm.de(R.Kimmich). 0926-2040/$-see front matter r 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2003.03.017