The word divulgement is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 24
Highest Scoring Words With Friends™ Play In The Letters
Seven Letter Word Alert: (31 words)
deeming, deleing, delving, detinue, diluent, divulge, dueling, eluding, eluting, emulged, evident, gentile, gentled, glinted, guilted, indulge, legumin, lenited, livened, meeting, melding, melting, mingled, munited, teeming, tingled, untiled, untimed, veinlet, veinule, vinelet