From Longman Dictionary of Contemporary Englishunquenchableun‧quench‧a‧ble /ʌnˈkwentʃəbəl/ adjective an unquenchable desire is one that is impossible to satisfy the seemingly unquenchable thirst (=desire) for Western art
Examples from the Corpus
unquenchable• Is not dread of thirst when your well is full, the thirst that is unquenchable?• The sudden urgent needs of her body came from her gypsy roots; fiery, desperate and unquenchable.• It filled his enemies with terror and his own troops with unshakeable faith and unquenchable blood lust.• Still Damocles worried and pecked, coated with blood and frantic with an apparently unquenchable desire to kill and kill again.• He has an unquenchable enthusiasm for hunting, and especially for hawking.• He gained a reputation as an eccentric but dependable officer of unquenchable high spirits.• This exotic potpourri stimulated his own love of natural things and his unquenchable interest in perfumes. 