DHC8 CAPT DEVIATES AROUND TSTM CELLS WITHOUT CLRNC RESULTING IN ENTERING ANOTHER ARTCC SECTOR'S AIRSPACE.

Narrative

WE WERE INBOUND TO GAINESVILLE; FL; FROM THE N. WE HAD BEEN FLYING NEARLY 2 HRS; AND WERE DEVIATING FOR WX IN THE AREA. WE WERE W OF COURSE; WITH THE LAST CLRNC BEING TO NAV DIRECT GAINESVILLE ARPT WHEN ABLE. I TURNED THE ACFT THROUGH SOME MODERATE TO HVY RAIN SHOWERS (VISUALLY AND WITH THE WX RADAR) TOWARDS GNV. AS I TURNED BACK TO THE L; WHICH WAS MORE OR LESS DIRECT THE FIELD; ANOTHER CELL WAS IN OUR WAY AND VERY CLOSE TO THE ACFT. WITHOUT FURTHER CLRNC FROM ATC TO DEV L; I TURNED THE ACFT L OF COURSE TO AVOID THE CELL. I THEN TOLD ATC WE WERE L OF COURSE NOW; AND WOULD TURN BACK DIRECT GNV WHEN ABLE. ATC SAID WE HAD JUST FLOWN INTO THE NEXT SECTOR'S AIRSPACE (WITHOUT THEM COORDINATING) AND THAT WE HAD NOT BEEN CLRED FOR A L DEV. I TOLD THEM AS WE TURNED DIRECT GNV; ANOTHER CELL WAS IN OUR WAY; WE HAD TO DEV A COUPLE MI TO MISS IT; AND COULD TAKE THE DIRECT TURN AGAIN SHORTLY. WE LANDED UNEVENTFULLY 15 MINS LATER. FACTORS TO THIS PROB WERE: WX (#1); ATC; (AND RUNNING LATE); ALONG WITH KEEPING THE ACFT OUT OF THE NUMEROUS CELLS TO GIVE THE PAX A DECENT RIDE.