4.2.4—SA:V ratio investigation

An agar-block investigation models how surface-area-to-volume ratio and diffusion distance affect exchange. Blocks with different dimensions are exposed to the same coloured or indicator solution, so the fraction reached or the penetration distance can be compared after a controlled exposure.

1. Prepare matched blocks: Make agar blocks of different dimensions from the same agar mixture and indicator/colour condition. Keep the block shape comparable and calculate each block’s surface area, volume and SA:V.
2. Set the fair comparison: Use the same external solution, temperature, volume and exposure time for every block. Handle and remove blocks consistently so the only planned difference is block size/SA:V.
3. Expose the blocks: Place the blocks in the solution so that the solution can reach all intended exposed surfaces. Use a control or reference condition where appropriate to identify the starting colour and any background change.
4. Measure the diffusion front: After exposure, section blocks consistently and measure penetration depth or the coloured fraction using the same rule for every block. Record the result rather than relying on a visual impression.
5. Repeat and compare: Repeat each block size, summarise variation and compare penetration or coloured fraction with calculated SA:V. A higher SA:V should expose a larger fraction of the block and shorten the average diffusion path in the fixed exposure.
6. State the model boundary: Agar shows a geometric diffusion pattern; it does not directly test a living cell’s membrane selectivity, active transport, metabolism or cytoplasm.

Diffusion proceeds inward from each exposed surface. A smaller block has more surface relative to its volume and a shorter distance to its centre, so the same exposure can reach a greater fraction of it than a larger block. The conclusion is about geometry and diffusion under matched conditions, not about a precise biological rate constant.

Do not compare blocks after different exposure times or with different agar/solution conditions. Colour reaching the centre shows indicator diffusion in agar; it is not evidence that agar has a cell membrane or that active transport occurred.