All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
According to the majority of scholars, one of the preconditions for the validity of an oath is for it to be verbalized loud enough for the oath-maker to hear himself. Al-Mawsoo‘ah Al-Fiqhiyyah Al-Kuwaitiyyah states about the preconditions of the validity of an oath: “The oath must be verbalized. According to the majority of scholars, self-talk (unspoken inner thought) is not sufficient; rather, it must be verbalized loud enough for the oath-maker to hear his own voice, if his hearing is not impaired and there are no impediments to hearing, like loud noise or blocked ears.
Stipulating as a condition for the validity of an oath that one hears himself when verbalizing the oath, even if constructively (in a non-obvious manner), is the opinion of the majority of the scholars. The Maaliki scholars as well as the Hanafi scholar Al-Karkhi held that hearing oneself is not a precondition (for the validity of the oath). What is rather required is to articulate the letters along with moving the tongue, even if he cannot hear his voice, nor someone else who is placing his ear near his mouth, in the absence of hearing impairment and impediments.” [End of quote]
In your case, it seems that you did not utter the wording of the oath, as this would be impossible with your lips closed, and therefore your oath is neither valid nor binding in the first place, and you are not liable for any expiation.
Allah Knows best.