## Abstract

Highly connected continuous phases in a porous medium fan usefully be described in terms of their connectivity. Appropriate descriptions of connectivity are the connectivity number density or the related quantity Euler number density. Broadly speaking, Euler number density is equal to the number of discrete objects which comprise the phase plus the number of enclosed cavities within those objects Less the number of tunnels through the objects, per unit volume. The conneulor is a convenient stereological method for estimating Euler number density The relevant probes (i.e. disectors) from which the estimate is obtained are randomly positioned and arbitrary orientated pairs of closely spaced parallel planes.

We have applied the conneulor method to estimate the Euler number density of the pore space in a cell of sintered silica imaged using a magnetic resonance (MR) microscope. By flooding the cell simultaneously with a mixture of oil and water prior to imaging we were able to obtain a series of 16 contiguous perfectly registered serial MR sections depicting the pore space. The Euler number density of the porous medium estimated from four systematic pairs of consecutive A IR images is -5.6 per mm(3) with a coefficient of error (CE) of 10-15%. The Euler number density was lower near the walls of the silica cell than the centre, which is consistent with the method of formation of the cell.

In contrast to the majority of stereological methods, and in common with the physical disector, the conneulor method requires that deductions are made regarding the changes in the morphology of the structure of interest that occur between the two parallel image planes comprising the sampling probe. We therefore compared estimates of the Euler number density of the pore space obtained by two independent observers. We conclude that careful thought and discussion between observers is required before a definitive set of counts is made. Once mastered the conneulor counting rules are straightforward to apply.

Original language | English |
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Pages (from-to) | 110-118 |

Number of pages | 9 |

Journal | Journal of Microscopy |

Volume | 187 |

Publication status | Published - Aug 1997 |

## Keywords

- connectivity number
- conneulor
- Euler number
- Euler-Poincare characteristics
- genus
- magnetic resonance imaging (MRI)
- microscopy
- porous media
- stereology
- UNBIASED ESTIMATION
- DENSITY
- NUMBER