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Special Topics - Modules in Pharmaceutical Engineering ChE 702

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1 Special Topics - Modules in Pharmaceutical Engineering ChE 702
Introduction to Mixing Equipment and Processes in Pharmaceutical Operations Piero M. Armenante 2008 ©

2 Objectives Become familiar with the principles of single and multiphase mixing in pharmaceutical processes Analyze pharmaceutical processes or in which mixing is important Provide basic tools to conduct process design analysis and scale-up of processes or in which mixing is important Piero M. Armenante ChE702

3 Relevant Topics Classification of Mixing Processes and Applications
Mixing Equipment Liquid Mixing Fundamentals Mixing and Blending in Low Viscosity Liquids High Viscosity Mixing in Stirred Tanks Mass Transfer and Mixing Solid-Liquid Mixing Piero M. Armenante ChE702

4 Relevant Topics (continued)
Liquid-Liquid Mixing Gas-Liquid Mixing Mixing and Chemical Reactions Heat Transfer Jet Mixing In-Line Mixing Mechanical Aspects of Mixing Systems Special Topics and Applications Piero M. Armenante ChE702

5 Classification of Mixing Processes and Applications

6 Instructional Objectives of This Section
By the end of this section you will be able to: Identify basic mixing classes Develop an appreciation for the importance of mixing in industry Provide examples of common pharmaceutical mixing processes Piero M. Armenante ChE702

7 Definition of Mixing Textbook definition:
The term “mixing” refers to all those operations that tend to reduce non- uniformity in one or more of the properties of a material in bulk (e.g., concentration, temperature) Piero M. Armenante ChE702

8 Example of Mixing Tanks/Reactors
Piero M. Armenante ChE702

9 Definition of Fluid Mixing
“Fluid mixing” refers to mixing operations in which the continuous phase is a fluid Although a gas can be used as a fluid (e.g., fluidization) a liquid is typically the continuous phase in fluid mixing processes In the rest of this course a liquid phase will always be the continuous phase Piero M. Armenante ChE702

10 Single-Phase vs. Multiphase Mixing
Single-phase mixing refers to mixing of miscible fluids. This operations is typically called “blending” Multiphase mixing refers to mixing immiscible phases, i.e.: solid-liquid mixing liquid-liquid mixing gas-liquid mixing Piero M. Armenante ChE702

11 Importance of Mixing in the Pharmaceutical Industry
Mixing of a fluid with other media (solids, liquids) is an extremely common operation encountered in countless applications in the pharmaceutical industry Many pharmaceutical processes require or are greatly enhanced by: rapid homogenization of miscible components (in single phase systems) intimate contact between two or more distinct phases (in multiphase systems) Piero M. Armenante ChE702

12 Examples of Typical Pharmaceutical Mixing Applications
Blending Precipitation and Crystallization Chemical reaction Fermentation Solid-liquid suspension Liquid-liquid emulsification Gas sparging Piero M. Armenante ChE702

13 Economic Impact of Mixing-Related Problems
The impact of poor mixing on industrial applications has been estimated to be at 1-10 billion $/year (1989) The additional economic impact associated with scale-up and start up problems, waste material and by-products generation has not been estimated yet Piero M. Armenante ChE702

14 Mixing as an Objective or a Means to an End
There are operations where mixing itself is the objective of the process These operations are required to produce homogenization of a system or a product Examples: Blending of gasoline in large storage tanks Dispersion of pigments in paint Uniform and stable suspension of API particles in an oral liquid dosage form Formation of stable liquid-liquid emulsions Piero M. Armenante ChE702

15 Mixing as an Objective or a Means to an End
However, in most pharmaceutical processes involving mixing, mixing is just a means to achieve a process objective In this case mixing is typically required to effectively conduct a primary process (NOT to be limited by mixing) Piero M. Armenante ChE702

16 Mixing as an Objective or a Means to an End
Examples of processes possibly affected by mixing: Dissolution of an intermediate in a stirred vessel prior to reaction (mass transfer) Precipitation of API or intermediate (crystallization) Minimization of impurity formation during synthesis of a drug product (parallel/consecutive homogeneous reaction) Suspension of a catalyst during heterogeneous catalysis (mass transfer + heterogeneous reaction) Preparation of nano/micro-particles or droplets of desired particle size distribution (particle size control) Achievement of a uniform temperature in a crystallizer and temperature control (heat transfer) Piero M. Armenante ChE702

17 Mixing as an Objective or a Means to an End
Mixing operation may involve: single phase liquids (e.g., blending of miscible solutions, fast chemical parallel reactions and impurity formation) multiphase systems (e.g., solid dispersion/suspension, emulsification) Mixing can improve both single-phase and mulpiphase processes Piero M. Armenante ChE702

18 Mixing as a Means to an End
Example: interfacial mass transfer Cinterface A Cbulk kL Piero M. Armenante ChE702

19 Mixing as a Means to an End
Example: interfacial mass transfer Mixing affects: state of dispersion or suspension of the dispersed phase, i.e., degree of macroscopic homogeneity of the dispersed phase throughout the continuous phase ( VL, DC) specific interfacial area (av), and overall interfacial area (A) mass transfer coefficient at the interface (kL) Piero M. Armenante ChE702

20 Mass Transfer Operations in Mixing Processes
All mass transfer processes are enhanced by: high mass transfer coefficients large interfacial area Mixing can contribute to achieve both However, most mixing operations are associated with the generation of interfacial (contact) area Piero M. Armenante ChE702

21 Classification of Mixing Processes
Piero M. Armenante ChE702

22 Mass Transfer Operations in Mixing Processes
Piero M. Armenante ChE702

23 Reactions in Mixing Processes
Piero M. Armenante ChE702

24 Single vs. Multiple Mixing Requirements
Mixing problems can involve: a single mixing requirement (e.g., suspend solids) multiple simultaneous mixing requirements (e.g., suspend solids, homogenize liquid phase, promote solid-liquid mass transfer, transfer heat) Even multiple requirements are typically satisfied by the use of a single impeller Piero M. Armenante ChE702

25 Example of Multiple Mixing Requirements: Crystallizers
In crystallizers a successful process depends on: heat transfer (for supersaturation) bulk blending (for homogenization) solids suspension (for crystal growth) effective mass transfer (for crystal growth) possible gas removal (boiling systems) Piero M. Armenante ChE702

26 Critical Mixing Process
Whenever a process involving a mixing operation is analyzed one should ask: is mixing a critical component of the process? if multiple, simultaneous mixing requirements are present which one is the most critical? Piero M. Armenante ChE702

27 Mixing Equipment

28 Instructional Objective of This Section
By the end of this section you will be able to: Identify basic types of mixing equipment Describe main components of mixing equipment Describe main features and characteristics of mixing equipment Piero M. Armenante ChE702

29 Classification of Mixing Equipment
Mixing is typically conducted with: mechanically stirred tanks jet mixed tanks in-line dynamic mixers in-line static mixers high-shear mixing equipment mixing equipment for highly viscous materials (e.g., polymers) Piero M. Armenante ChE702

30 Mechanically Stirred Tanks and Reactors
Motor Gearbox Shaft Baffle Impeller Piero M. Armenante ChE702

31 Drive (Motor-Gearbox) Assembly
After Chemineer Piero M. Armenante ChE702

32 Mechanically Stirred Tanks and Reactors: Symbols
Cb D T Piero M. Armenante ChE702

33 Mechanically Stirred Tanks and Reactors: Symbols
Cb T Piero M. Armenante ChE702

34 Mechanically Stirred Tanks: Nomenclature
Tank shape = cylindrical (occasionally square cross section) T = Internal diameter of tank HT = Internal height of tank H = Z = Liquid height B = Baffle width Piero M. Armenante ChE702

35 Mechanically Stirred Tanks : Other Geometric Characteristics
Shape of tank bottom (flat, dished, conical, hemispherical) Baffle length (full, half) Number of baffles Baffle position Gap between baffles and tank (B) Gap between baffles and tank bottom Piero M. Armenante ChE702

36 Baffles Baffles are typically introduced to prevent vortex formation and convert tangential (rotational) flow into axial (vertical) flow Baffles are always used in turbulent flow systems (low viscosity fluids) Baffles are not used in laminar flow (high viscosity fluids) Piero M. Armenante ChE702

37 Baffles Typically four baffles are used (occasionally three) in fully baffled tanks In glass-lined tanks a single baffle placed midway between the tank wall and the impeller may be used A gap between the baffles and the wall is introduced to prevent stagnation behind the baffles and accumulation of material (e.g., solids) Piero M. Armenante ChE702

38 Typical Baffle Arrangement in a Stirred Tank
Piero M. Armenante ChE702

39 Typical Baffle Arrangement in a Glass-Lined Tank
De Dietrich Vessel Single Baffle Piero M. Armenante ChE702

40 Baffles and Vortexing Baffled tank: No vortex Unbaffled tank: Vortex
Piero M. Armenante ChE702

41 The “Standard” Tank H/T = 1 D/T = 1/3 C/D = 1
B/T = 1/10 (academic) or 1/12 (industry) Number of baffles = 4 Baffle length = full B/T =1/72 or 1/100 Bottom shape = flat Piero M. Armenante ChE702

42 Impellers After Oldshue, 1984 Piero M. Armenante ChE702

43 Impeller Types Impeller can be classified as follows:
radial impellers (e.g, Rushton turbines, paddles, flat-blade turbines, Smith impellers) axial impellers (e.g., marine propellers, pitched-blade turbines, fluidfoil impellers such as HE-3s, A-310s) close-clearance impeller (e.g., anchors, helical ribbons, gates) Piero M. Armenante ChE702

44 Radial Impellers Radial impellers pump radially.
They are used primarily with low-viscosity liquids in baffled tanks. Disk turbines can be used for gas dispersion. Piero M. Armenante ChE702

45 Radial Impellers Common types include:
Rushton turbine (6-blade disk turbine) paddle flat-blade turbines curve-blade turbine retreat-blade turbine Smith impeller Piero M. Armenante ChE702

46 Examples of Radial Flow Impellers
After Tatterson, 1991 Piero M. Armenante ChE702

47 Examples of Radial Flow Impellers
Disk Turbine (Rushton Turbine) Piero M. Armenante ChE702

48 Examples of Radial Flow Impellers
Flat-blade turbine (Source: Chemineer) Piero M. Armenante ChE702

49 Example of Radial Flow Impeller for High Shear Applications
R500 Sawtooth Impeller (Source: Lightnin) Piero M. Armenante ChE702

50 Example of Radial Flow Impeller for Gas Dispersion
Concave-Blade Turbine (Smith Turbine) Piero M. Armenante ChE702

51 Example of Radial Flow Impeller for Gas Dispersion
Concave-Blade Turbine (Smith Turbine) Piero M. Armenante ChE702

52 Flow Generated by Radial Impellers
Piero M. Armenante ChE702

53 Flow Generated by a Radial Impeller in a Stirred Tank
After Tatterson, 1991 Piero M. Armenante ChE702

54 Axial Impellers Axial impellers pump primarily (but not exclusively) vertically, either upwards or downwards. They are used mainly with low-viscosity liquids in baffled tanks. They are typically used in a downpumping mode. High-solidity impellers are used with gas. Piero M. Armenante ChE702

55 Pitch Ratio in Axial Impellers
The pitch-to-diameter ratio (or “pitch ratio”) is the ratio of the distance the impeller would advance per rotation to the impeller diameter In constant pitch impellers (e.g., propellers) the angle of attach changes along the blade; in variable pitch impellers (e.g, 45° pitched-blade turbine) the angle is constant Piero M. Armenante ChE702

56 Constant vs. Variable Pitch
Constant Pitch (Variable angle of attack) Variable Pitch (Constant angle of attack) After Oldshue, 1984 Piero M. Armenante ChE702

57 Axial Impellers Common types include: marine propeller
pitched-blade turbine fluidfoil impeller (e.g., Chemineer HE3, Lightning A-310) high-solidity ratio impellers (e.g., Prochem) Piero M. Armenante ChE702

58 Examples of Axial Flow Impellers
After Tatterson, 1991 Piero M. Armenante ChE702

59 Examples of Axial Flow Impellers
Pitched-Blade Turbine Piero M. Armenante ChE702

60 Example of Axial Flow (Hydrofoil) Impeller
Chemineer SC-3 Impeller Piero M. Armenante ChE702

61 Example of Axial Flow (Hydrofoil) Impeller
Chemineer HE-3 Impeller Piero M. Armenante ChE702

62 Example of Axial Flow (Hydrofoil) Impeller
Chemineer HE-3 Impeller Piero M. Armenante ChE702

63 Example of Axial Flow (Hydrofoil) Impeller
Maxflow W Impeller Piero M. Armenante ChE702

64 Example of Glassed Impellers
De Dietrich GlasLock System Piero M. Armenante ChE702

65 Flow Generated by Axial Impellers
Flow generated by mixed-flow impellers (e.g., 45° pitched-blade turbine) Flow generated by true axial impellers (~propeller, A-310, HE-3) Piero M. Armenante ChE702

66 Flow Generated by an Axial Impeller in a Stirred Tank
After Tatterson, 1991 Piero M. Armenante ChE702

67 Close-Clearance Impellers
Close-clearance impellers are primarily used with high-viscosity fluids in unbaffled tanks. Close-clearance impellers scrape fluid off the tank wall and off the impeller. They generate a complex flow pattern and have a pumping action similar to that of a displacement pump. Piero M. Armenante ChE702

68 Close-Clearance Impellers
Common close-clearance impeller types include: anchors helical ribbons gates kneaders Z- and sigma-blade impellers Piero M. Armenante ChE702

69 Examples of Close Clearance Impellers
Anchor Impeller (Source: Chemineer) Piero M. Armenante ChE702

70 Examples of Close Clearance Impellers
After Oldshue, 1984 Piero M. Armenante ChE702

71 Examples of Close Clearance Impellers
After Oldshue, 1984 Piero M. Armenante ChE702

72 Examples of Close Clearance Impellers
Double Helical Ribbon Impeller (Source: Chemineer) Piero M. Armenante ChE702

73 Examples of Close Clearance Impellers
Auger Impeller (Source: Chemineer) Piero M. Armenante ChE702

74 Examples of Close Clearance Impellers
After Tatterson, 1991 Piero M. Armenante ChE702

75 Examples of Close Clearance Agitation System
Piero M. Armenante ChE702

76 Blending Capabilities of Different Impellers
Piero M. Armenante ChE702

77 Characteristics of Common Radial Impellers
Rushton turbines (Disk turbine, R-100). Strong radial flow, high power consumption, significant shear, good for gas dispersion Smith impeller. Similar in performance to Rushton turbine, but particularly well suited for gas dispersion Piero M. Armenante ChE702

78 Characteristics of Common Radial Impellers
Paddles. Simple and inexpensive, medium-to-strong radial flow and shear, intermediate power consumption, good for simple applications at small-to-medium scales Flat-blade turbines. Similar to paddles but with stronger radial flow power, consumption, and shear. Used in transition flow. Piero M. Armenante ChE702

79 Characteristics of Common Radial Impellers
Curve-blade turbine. Similar to flat- blade turbines Retreat-blade impeller (Pfaudler, De Dietrich types). Simpler construction suitable for glass-lined vessels; reduced power and flow Piero M. Armenante ChE702

80 Characteristics of Common Axial Impellers
Marine propeller (A-100). Oldest constant-pitched impeller, usually cast (cannot be easily inserted in a manhole), expensive, low power consumption, high pumping rate Pitched-blade turbine (A-200). Very common, simple, usually 45°, effective for solid suspension; mixed flow; medium power consumption, good pumping rate Piero M. Armenante ChE702

81 Characteristics of Common Axial Impellers
Fluidfoil impellers. Many types exist (Chemineer HE-3, Lightning A-310); expensive, near constant pitch for improved axial flow, low power consumption, high pumping rate High-solidity ratio impellers. Many types exist (e.g., Maxchem); low-to-medium power consumption, high pumping rate, “streamlined” Piero M. Armenante ChE702

82 Characteristics of Common Close-Clearance Impellers
Anchor impellers (A-400). Good for blending and heat transfer for liquids with 5000 cP <  < 50,000 cP Helical ribbon. Good for blending high viscosity liquids (up to 25·106 cP) Gates. Used in large “squat” tanks. Kneaders, Z- and sigma-blade impellers. Used to mix pastes Piero M. Armenante ChE702

83 Impellers: Nomenclature
D = Impeller diameter C = Impeller clearance off the tank bottom measured from the impeller center Cb = Impeller clearance off the tank bottom measured from the bottom of the impeller Sij = distance between i and j impellers Piero M. Armenante ChE702

84 Impellers: Nomenclature
L = Impeller blade length w = Impeller blade width wb = Impeller blade width projected along the vertical axis Sij = distance between impellers i and j  = Blade angle of attack (if constant) Pitch Piero M. Armenante ChE702

85 Rushton Turbine L/D=1/4 w/D=1/5 Disk diameter= 3/4·D or 2/3 ·D
Piero M. Armenante ChE702

86 45° Pitched-Blade Turbine
Piero M. Armenante ChE702

87 Typical Ranges for Geometric Variables
T = 0.1 m to 10 m (0.3’-33’) H/T = 0.3 to 1.2 for single impeller systems D/T = 1/5 to 2/3 C/D  1 B/T = 1/10 to 1/12 Piero M. Armenante ChE702

88 Jet Mixers Jet mixers rely on the use of a jet, i.e., a stream of liquid injected at high velocity in the bulk of another miscible liquid. This is typically achieved with an external recirculation pump Jet mixers are used in: tanks tubes and pipes Piero M. Armenante ChE702

89 External recirculation line
Jet Mixer External recirculation line Pump Piero M. Armenante ChE702

90 Jet Mixers in Tanks Jet mixers are typically used in large tanks.
Jet mixers are used for blending purposes (e.g., gasoline) or to suspend solids in unusual processes (e.g., radioactive material slurry). Typically one or more jets are placed at an angle to provide good recirculation. Piero M. Armenante ChE702

91 Axial Jets in Mixing Tanks
Poorly mixed zone Piero M. Armenante ChE702

92 Angled Jets in Mixing Tanks
Poorly mixed zone Piero M. Armenante ChE702

93 In-Line Mixers In-line mixers are small mixing devices placed in the same line where the materials to be mixed are flowing. Two types of in-line mixers exist: dynamic mixers, where the mixing energy is provided from the outside static (motionless) mixers where the fluid itself provides the mixing energy Piero M. Armenante ChE702

94 In-Line Dynamic Mixers
In-line dynamic mixers consist of small high-speed mixers placed inside a casing fed with a continuous stream of the materials to be mixed. The residence time of in-line mixers is usually of the order of seconds. Piero M. Armenante ChE702

95 Example of a Dynamic In-Line Mixer
Piero M. Armenante ChE702

96 Example of In-Line, High Shear, Homogenizing Mixer
Greerco (Chemineer) Piero M. Armenante ChE702

97 Example of a Two-Stage Rotor Stator for In-Line High Shear Mixer
Greerco (Chemineer) Piero M. Armenante ChE702

98 Applications of Dynamic In-Line Mixers
After Oldshue, 1984 Piero M. Armenante ChE702

99 In-Line Static Mixers Static mixers consist of mirror image inserts (elements) placed inside a pipe, capable of altering the fluid flow, and rearranging the distribution of fluid elements across the pipe cross section. Static mixers are only capable of homogenizing the content of the pipe across its cross section but not along its length. Piero M. Armenante ChE702

100 Static Mixers Source: Chemineer Piero M. Armenante ChE702

101 Classification of Static Mixers
Static mixers are classified according to the flow regime under which they operate. Static mixers are available for: laminar flow transitional flow turbulent flow Piero M. Armenante ChE702

102 Static Mixers for Laminar Flow
In laminar flow the only mechanism for radial mixing is molecular diffusion. Each element in a laminar static mixers typically produces spit and a rotation (90° or 180°) of the flow, which is then fed to the next element. Such actions result in further sub-divisions of the flow and the generation of striations leading to mixing. Piero M. Armenante ChE702

103 Static Helical Mixer for Laminar Flow
After Myers et al., Chem. Eng. June 1997 Piero M. Armenante ChE702

104 Static Helical Mixer for Laminar Flow
Piero M. Armenante ChE702

105 Static Helical Mixer for Laminar Flow
Piero M. Armenante ChE702

106 Static Mixers for Turbulent Flow
In turbulent flow, turbulent eddies are responsible for radial mixing Flow in open pipes produces radial mixing if enough pipe length is provided (at least 100 pipe diameters) Static mixers for turbulent flow rely on vortex generation to produce mixing Piero M. Armenante ChE702

107 Static Vortex Mixer for Turbulent Flow
Piero M. Armenante ChE702

108 Static Vortex Mixer for Turbulent Flow
Source: Chemineer Piero M. Armenante ChE702

109 Static Vortex Mixer for Turbulent Flow
After Myers et al., Chem. Eng. June 1997 Piero M. Armenante ChE702

110 High-Shear Mixing Equipment
High-shear mixers are devices used to generate high velocity gradients across small distances (resulting in high shear stress and shear rates) in order to disperse, break up, or homogenize a second immiscible phase. Different devices base on different physical mechanisms are used to produce high shear. Piero M. Armenante ChE702

111 High-Shear Equipment High shear equipment include:
(high speed) rotor-stator devices valve homogeneizers, such as: valve homogeneizers ultrasonic homogenizers Piero M. Armenante ChE702

112 High-Speed, High-Shear Rotor-Stator Mixer
High-speed rotor-stator mixers are devices in which a rotor rotates at high speed inside a casing provided with slots. A small gap exists between the rotor and the stator. As the liquid (and its dispersed phase) move through the rotor-stator assembly they are subjected to high shear, resulting in break up effects. Piero M. Armenante ChE702

113 High-Speed, High-Shear Rotor-Stator Mixer
Piero M. Armenante ChE702

114 Example of High-Speed, High-Shear Rotor-Stator Mixer
Silverson Machines, Inc. Piero M. Armenante ChE702

115 Example of High-Speed, High-Shear Rotor-Stator Mixer
Silverson Machines, Inc. Piero M. Armenante ChE702

116 Example of High-Speed, High-Shear Rotor-Stator Mixer
Silverson Machines, Inc. Piero M. Armenante ChE702

117 Colloid Mills Colloid mills are in-line machines designed to finely homogenize, disperse solids, and emulsify immiscible liquids Mixing head consist of a rotor and a stator separated by an extremely small gap ( in.) Stirring speed are usually extremely high ( ,000 rpm) Flow rates are usually small (as a result of the small rotor-stator gap) Piero M. Armenante ChE702

118 Colloid Mill Greerco (Chemineer) Piero M. Armenante ChE702

119 Colloid Mill Greerco (Chemineer) Piero M. Armenante ChE702

120 Colloid Mill IKA® Piero M. Armenante ChE702

121 Colloid Mill Greerco (Chemineer) Piero M. Armenante ChE702

122 Valve Homogenizers Valve homogenizers pump material at high pressure ( bar) through small orifices. The high velocity in the orifices produces high shear. The equipment operates in line and can be used to produce emulsions, dispersion, and suspensions. Piero M. Armenante ChE702

123 Valve Homogenizer After Harnby et al., 1985 Piero M. Armenante ChE702

124 Example of Valve Homogenizer
Five Star Technologies Piero M. Armenante ChE702

125 Ultrasonic Homogenizers
Ultrasonic homogenizers pump material at high pressure (up to 150 bar) through a small orifice placed in front of a vibrating ultrasonic blade. The high velocity in the orifice produces high shear, and the blade produces microcavitation that results in emulsions, dispersion, and suspensions of the dispersed phase. Piero M. Armenante ChE702

126 Ultrasonic Homogenizer
After Harnby et al., 1985 Piero M. Armenante ChE702

127 Basic Mechanisms in Laminar Flow Mixing
Laminar shear Elongation and extensional flow Distributive mixing Molecular diffusion Stresses in laminar flow Piero M. Armenante ChE702

128 Mixing Equipment for Highly Viscous Materials
Equipment for highly viscous material (such as pastes, dough, plastics) include: kneaders single-screw extruders twin-screw extruders Piero M. Armenante ChE702

129 Double-Arm Kneader After Perry and Green, 1984 Piero M. Armenante
ChE702

130 Single-Screw Extruder
Feed Hopper Die Piero M. Armenante ChE702

131 Twin-Screw Extruder Piero M. Armenante ChE702

132 Single-Screw Extruder
Piero M. Armenante ChE702

133 Screw Design to Enhance Mixing/Compounding Capability in Single Screw Extruders
Piero M. Armenante ChE702

134 Twin-Screw Extruder with Clam-Shell Barrel Design
Piero M. Armenante ChE702

135 Gear Mixing Elements in a Twin-Screw Extruder
Piero M. Armenante ChE702

136 Kneading Paddles in a Twin-Screw Extruder
Piero M. Armenante ChE702

137 Final Remarks About Impellers
No universal “optimal” impeller design exists Each process needs to be analyzed to determine what are the controlling mechanisms Impellers can be designed to optimize the process Piero M. Armenante ChE702


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