What is a fine-tooth rat-tail comb used for?

A rat-tail comb has fine teeth and a long pointed tail. The fine teeth smooth, part and finish, while the tail lifts and separates clean sections — ideal for precise parting, blow-drying and styling fine, straight or thin hair.

Is a fine-tooth comb suitable for thick or curly hair?

Not for detangling — closely-spaced fine teeth tend to snag and pull thick or curly hair. For those hair types a coarse-tooth or wide-tooth comb is gentler and more effective.

Will an aluminium comb rust?

No. The comb is anodized, so unlike a stainless steel comb it won't rust or stain. You can clean it with soap and water, or even boil it to sterilise, without harming the finish.