Power requirement of solid mixers is influenced in a complicated manner by various factors, such as the operating conditions, the properties of the powders, the dimension of the mixers, and so on.
In the present work, the relation between the torque of the horizontal mixers and those factors has been studied.
The torque increases with increasing the charged ratio, f, the bulk density, ρ_a and the internal friction factor, μ_i of the powders, and the dimension of the mixer. On the other hand, the torque is not influenced by the rotating speed, N, in the range of 30≤N≤200r.p.m. The shear force has been found to be a dominant factor in the total power requirement of the mixer.
The power data are well correlated with the experimental conditions by the relation Pg_c=1.3μ_iρ_adf(φD₀²L)d_eN_s d_e=[πL/4{2/P₀(D₀²-(D₀-2b₀)²)+1/P_i(D_i²-(D_i-2b_i)²)}]^1/2 where D: diameter, L: length, b: width, P_{i, 0}: pitch, N_s: rotating speed, all in M. K. S. units, and suffices “0” and “i” refer to the outer and inner ribbon.

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The effects of various operating conditions on the rotational torque of vertical ribbon mixers have been studied.
The rotational torque, T[Kgm] of the mixers increases with increasing the height of powders bed, H[m], the bulk density, ρ_a[kg/m³] and the internal friction factor μ_i[-] of the powders, and the diameter of the ribbon, D₀[m]. In the range of the rotating speed, N, of 30≤N≤100r.p.m., the torque remains almost constant and has a tendency to decrease as the ribbon width increases.
The torque data are well correlated with the experimental conditions by the relation T=0.15ρ_a^1.0μ_i^0.7R_p^1.2R_b^-0.8H^1.5D₀^3.0, where, R_p [-] and R_b [-], respectively, are the ratios of the pitch and the width of the ribbon to the ribbon diameter.

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Power requirement for agitating a powders bed in a vertical ribbon mixer has been analyzed by introducing a simplified model, which regards the motion of the helical ribbon blade as that of a flat plate.
The total force exerted on the blade by the powders bed is assumed to be the sum of; (i) the pressure force by the powders bed in the passive Rankine state, (ii) the shear force acting on the circumscribed cylindrical surfaces about the ribbon blade, and (iii) the inertia force for accelerating the powders mass surrounded by the cylindrical surfaces. Among these forces, the shear force has been dominant.
This assumption leads to the equation
N_P=K₀N_M^-1+K₃
The ratio of the total force to the inertia force, N_P and the ratio of the inertia force to the shear force, N_M are calculated and N_P is plotted against N_M^-1.
The coefficients, K₀ and K₃, were determined experimentally as; K₀=1.08 and K₃=0.025. An agreement within an accuracy of ±20% was obtained between the measured power and the one predicted by this equation.

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