Selection of pressure gradient in LBM

Dear all,
I was simulating pressure driven poiseiulle flow and I found that when i vary density difference less than 10^-6 or more than 0.1, code was not giving correct results. As i can’t suspect on the code because in the range of density difference 0.1 to 10^-6 our results were matching with analytical solution. Can anybody please help me out of this problem? I need to sort out this problem because in my research I will need very less density difference for simulation.