MANUFACTURE Therefore, the choice of tools and the
process are both critical elements that must be studied at an early stage to produce a mixture that meets your expectations. Yet it is also necessary to consider industrial scale-up when developing your formulations in the laboratory. For example, making a mixture with an
emulsifier whose rotation speed is 20,000 rpm is undoubtedly advantageous for saving time in the laboratory. Still, it does not make sense if the formulated product is produced on an industrial scale.
Succeeding in industrial scale-up For each new development or new formulation of cosmetic products, the transition from the laboratory to industrial production is essential. Industrial scale-up must integrate process parameters as far upstream as possible. The choice of these parameters, which partly depends on the mixer chosen, must be made very early. In the laboratory, the challenge is to
achieve the desired product and produce it on an industrial scale. This scale-up work is even more complicated as it involves different parameters. Therefore, from a laboratory mixer, it is a question of extrapolating the process to produce greater capacity. Controlling the performance of all the operations is also at stake.
What similarity to choose when extrapolating? Successful scale-ups key points are the invariant parameters or the principle of similarity and a homothety integrating two or three manufacturing capacities (bench/pilot/ industry). This principle of similarity can be of different orders.
A constant dimensional ratio: the geometric similarity The geometric similarity will apply a homothety on the tools and the tank and more precisely on their size. All the geometric dimensions between the two scales have the same relationship, called K or scale factor. The tool geometry obtains the ratio K. If
this invariant number is above 20, it can be considered unreliable extrapolation similarity and reliable if it is less than 10.
A constant speed ratio: the cinematic similarity The cinematic similarity consists of
T0
77
N° T0 N
H V
D T
V W
H° V V W°
D° T°
Geometric similarity: example of an application of the scale factor
extrapolating the rotating tool’s peripheral speeds and can be used when speed is the significant parameter to be considered in the process, e.g. for shearing needs, dispersion and emulsification processes. The peripheral speed or Vp results from
the following formula: Vp (m/s) = πND, where N is the speed of rotation of the tool, and D its diameter. The peripheral speed is expressed here in meters per second. We will then vary N1
to N2 and D1 to D2 . The
homothetic rule will not be the same for these last two parameters, since the tool increases in size, it will then be necessary to slow down its rotation speed to maintain the same peripheral speed Vp.
A constant forces ratio: the dynamic similarity Finally, other dynamic similarities must be considered, such as the forces between any point on two scales: pressure in the tank, friction, or inertia. The invariant or ratio results from the
recirculation rate or the power density, which is an essential criterion in the homogenization process.
REYNOLDS Re2 = Re1 ⇒
N2 D2 μ
FROUDE Fr2 = Fr1 ⇒ N2 2
ρ N2 D1 =
μ
2 D2 g
= N1
2 D1 g
2 ρ ⇒
N2 N1
⇒
N2 N1
=
D1 D2
=
D1 D2
2
Essential elements to remember for successful transposition As previously mentioned, it is essential in the laboratory to know and to choose the right ‘process’ operating conditions of its formulation.
Choice of similarity Depending on the process, it is necessary to choose the most relevant similarity typology. The incompatibility of specific parameters illustrates this choice, such as the dimensionless Reynolds and Froude numbers (Figure 1). The Reynolds number characterizes the flow of fluids, on which viscosity depends. From this number, it is possible to deduce a turbine diameter to be used (D1
to D2 ). This
same ratio will then be different if calculated from the Froude number, which characterizes the cinematic energy of a fluid relative to its gravitational energy.
1/2
Conclusion Scaling up is always a compromise between the different parameters involved. It is essential to understand them well, whether it is a question of process or equipment parameters or the calculated similarity principle. From bench to pilot to industrial mixing solutions, a range of mixing equipment with a consistent design will facilitate the transition from laboratory to industrial scale. It is recommended to try out technologies, analyze formulations and optimize the process to the fullest before scaling-up. Mixing equipment manufacturers can
Figure 1: With Reynolds and Froude numbers, it is possible to deduce a turbine diameter to be used
www.personalcaremagazine.com
help cosmetic and healthcare manufacturers choose the right equipment to achieve their goals.
PC June 2022 PERSONAL CARE
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88
