Are the sub wallets within a HD wallet visibly linked on the blockchain

[P Jones]

I am using the Mycelium app and i would like to know if i have two wallets within one account (i.e both backed up by the same seed) and one wallet has Bitcoin bought from an ATM with cash, there for anonymous and the other wallet has Bitcoin bought from an exchange using my master card and ID, therefore traceable to me. Does that then deanonymize the Bitcoin bough with cash?

[Xynerise]

It depends.
They aren't linked prima facie so no one can say that address 1xxx and 1yyy were generated from the same seed and are present in the same wallet.

It can be linked if you combine inputs for a transaction though, that suggests that the same person has the private keys to both addresses.

For example if you received 0.4BTC in address 1xxx and received 0.6 BTC 1yyy and want to make a 0.8 BTC payment.
Your wallet will combine inputs from both 1xxx and 1yyy to complete the transaction, and if your identity has been linked to 1xxx for instance, and it is combined in a transaction with 1yyy then it suggests that the same person owns both addresses (excluding coinjoin transactions)

[bob123]

Like Xynerise already mentioned how your privacy can get lost between several addresses when not taking care of the transactions created.
But myceliums wallets/accounts are independent from each other. Since you are not able to create a transaction using inputs from 2 different accounts of your mycelium app,
you won't be able to link them in one transaction. This keeps your BTC 'split'. Its foolproof. Just don't confuse your several HD wallets.