Scale-up model describing the impact of lubrication on tablet tensile strength

Lubrication of 2:1 and 1:1 blends of microcrystalline cellulose and spray-dried lactose or dibasic calcium phosphate (DCP) with 0.33% or 1% magnesium stearate, as model free-flowing pharmaceutical formulations, was performed in rotary drum blenders. Blender process parameters examined in this study included type (Bin, V, and Turbula), volume (0.75-Quart to 200-L), fraction of headspace in the blender after the blend is loaded (30–70%), speed (6–202 rpm), and time (up to 225 min). Based on analysis of the experimental data, the following model for the impact of the lubrication process on tablet tensile strength at 0.85 solid fraction, TSSF=0.85, was obtained, TSSF=0.85=TSSF=0.85,0[β exp(−γ×V1/3×Fheadspace×r)+(1−β)]TSSF=0.85=TSSF=0.85,0β exp−γ×V1/3×Fheadspace×r+1−β, where V is blender volume, Fheadspace is the headspace fraction, r is the number of revolutions (i.e. speed × time), TSSF=0.85,0 is the initial tensile strength of the blend, β is the sensitivity of the blend to lubrication, and γ is the lubrication rate constant of the formulation. This model can be used to maintain tensile strength during scale-up, by ensuring that (V1/3Fheadspacer)1 = (V1/3Fheadspacer)2. The model also suggests that formulations with DCP are less sensitive to lubrication and more slowly lubricated than formulations with spray-dried lactose (i.e. smaller β and γ values).