For example, in the iodine and starch reaction, if I use 20 mL of a set concentration of each, will it be slower to completion if I use 40 mL of each at the same concentration?
If you define "completion" by a certain percentage of conversion then no, they will behave exactly the same, provided that things like cooling and stirring are the same in both systems.
Here some elements to add to your reflection:
- Some chemicals (among them, many bio-polymers or proteins) can highly change fluid properties (mainly viscosity and surface tension) when dissolved, like you can see when solubizing Starch;
- Sheer stress affects viscosity of non-Newtonian fluids (moderate concentrations of starch are not Newtonian fluids, looks like jelly), and then chemical advection and diffusion. Thus it can affect reaction rate by modifying mass transfer rate;
- Sheer stress may change protein or polymer conformations (think about Starch which is a polymer) and then can affect their physical or chemical properties (eg.: it can produce foam a complex polyphasic system, or denature protein).
- Dark-purple color you see when mixing Iodine with Starch comes from a very specific complex of Iodine-Starch chains;
- Practically, you will apply sheer stress differently to a tank about 1L than 1000L.
Regarding to that aspects, it explains why sheer stress may impact reaction rates, in your case: Iodine Starch complex coordination reaction rate.