For simplicities sake, lets say Everyone at the table has $100, blinds are $0.50/$1.00.

Hero is dealt: 9s As
Villain is dealt: 10h 10d (Lets say I know this)

Preflop: Villain is UTG + 1 and raises to $5. Hero is on the button and calls $5. Everyone else folded.

Pot is now $11.50

Flop: 8s 10s 4h

(I have 9 outs total)

Villain bets $12
Hero calls $12

Pot: $35.50

Turn: Qs

Villain bets $12
Hero ???

The question is: How much do I have to raise him to give him bad odds to call and ultimately profit in the long run. He has 10 outs out of 46 total cards (21.7%). We both still have $83 (he has $71 after the turn bet). What is the right amount to raise here? Give math reasoning please.