Length Weight Fiber Distribution

One of many ways to characterize fiber mats is by the average fiber diameter distribution. There are many ways to define the average fiber but most appropriate for filter media is the length weighted average fiber size and fiber distribution.  Other average fiber diameters are used, such as a number distribution but the number distribution does not account for fibers of different lengths.

The length weighted fiber diameter is defined as the sum of the fiber diameters times length divided by the sum of the lengths

This average fiber diameter represents the mean fiber size of a distribution of fiber diameters.  To determine the frequency distribution you can use images of the fiber mats to measure diameters and lengths. The log normal frequency distribution fits the data better than normal frequency distribution for some applications such as electrospun nanofibers [1]. 

The normal frequency distribution is given by

where  is the standard deviation

The log normal frequency distribution is defined a bit different as

where the log mean diameters is given by

and the log standard deviation is given by

To measure fibers from a microscopic image, there are many free software programs available.  In our work we use a program called ImageJ (http://rsb.info.nih.gov/ij/) to measure length and diameter of fiber.  This program measures the number of pixels in the picture and the scales lengths according to the calibration provided by the user. The picture in Figure 1 shows an example fiber length and fiber diameter from a Scanning Electron Microscope image.

Multiple images may be necessary to obtain a sufficient number of measured fibers. We suggest no fewer than 300 fibers from 10 sample photographs taken at different locations on the fiber mat.