## Fig xA Optimization of the pitch

3. Results and discussion

3.1. Optimization of UADE parameters

3.1.1. Optimization of the pitch and diameter of the screw shaft via mathematical modeling

A schematic diagram of the UADE CUDC-907 shown in Fig. 2(a); an exploded diagram is shown in Fig. 2(b), and a cutaway diagram is shown in Fig. 2(c). Because the main component of the UADE is a modified screw propeller, the pitch and diameter of the screw shaft are important parameters. The effect of the pitch was evaluated as shown in the diagram of the movement states of the plant material in the cylindrical extractor with different pitches [Fig. 3(a and b)]. In multinucleate study, the pitch and diameter of the screw shaft were optimized via mathematical modeling. The efficiency of the screw conveyor is expressed as follows [23]:equation(3.1)η0=∫d2D24x2tanαxdx∫d2D2tan(αx+ρ)dxwhere η0 is the mechanical efficiency; αx is the lead angle; D is the nominal diameter of the spiral blade; d is the diameter of the screw shaft ( Fig. 2(c)); ρ is the equivalent friction angle; and dx is the width of the micro-membered ring.