Mixing of powders in rapid mixing granulator is counted in term of minutes or second and wetting of powders during kneading stage in rapid mixing granulator is also counted in minutes or second but did you ever think that the counting of mixing in term of time is not always the right practice especially when we talk about the batch size scale up from small scale equipment to large scale equipment.

During batch scale up there will be a trouble if we count mixing or kneading in terms of minutes or second because we have no data for the mixing time estimation for the scale up batch.

**Conventional Practice**

The conventional practice for mixing time of powders during batch size enhancement is to use the same mixing time for scale up as it was used previously for the small scale batch.

In conventional methods we have no scientific data or justification for this mixing time estimation of the scale up batch.

That is why the term tip speed plays an important role for the mixing time estimation and it has great importance in the pharmaceutical industry.

**What is the tip speed?Â **

The measure of the distance traveled by the tip of the impeller blade in a rapid mixing granulator at defined RPM in a specific time is known as tip speed.

In other words the total distance traveled by the tip of the impeller blade in the mixing bowl of a rapid mixing granulator in a specific time at a set RPM is known as tip speed.

**Explanation**

In tip speed we check how much (distance) meter mixing of the specific product in an equipment is done at a defined RPM & time.

Then we use the same distance to scale up the batch & calculate mixing time accordingly.

Meaning if we are shifting from a low capacity high shear mixing granulator to a high capacity rapid mixing granulator then due to the large diameter of the impeller blades the long distance will be covered in short time & we will calculate mixing time accordingly.

**Unit Of Tip SpeedÂ **

Tip speed is measured in following units

- Feet/minute
- Metre/SecÂ

**How to calculate tips speedÂ **

Tip speed calculation is done by the given formula,

**Ï€ Ã— d Ã— n / 60**

- d=diameter of impeller blade
- n= RPM of impeller bladesÂ
- Ï€=3.142

Ï€ has the constant value 3.142 & 60 is used to convert minutes into seconds.

**Example**

Suppose we are going to scale up our batch or we are going to change our equipment from low capacity to high capacity.

**Case Study 1Â **

Suppose we are using a rapid mixing granulator of 400 liters for our product and its batch size is 150 kilograms.

Now we are going to shift from 400 liters of rapid mixing granulator to 1200 liters of rapid mixing granulator where our total batch size will be 450 kilograms.

Now we will calculate the tip speed for both rapid mixing granulators and determine the mixing time for the scale up batchÂ size.

**Tip Speed For 400 liters RMG**

First of all we will calculate tip speed for 400 liters of rapid mixing granulator.

Suppose the diameter of impeller blades of 400 liters rapid mixing granulator is 0.3 meter.

The RMG is running at the speed of 75 RMPs.

To calculate the tip tip use the above formula & put values

**Tip Speed= Ï€ Ã— d Ã— n / 60**

Tip speed = 3.142 Ã— 0.3 Ã— 75 / 60

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.178 meter/sec

**ResultsÂ **

The tip speed in the case of 400 liters of RMG is 1.178 meter per second.

Now if our mixing time is 360 seconds for 150 kg batch then total distance traveled by the impeller blades tip will be as follow

**Total Distance = 1.178 Ã— 360**

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 424.08 meter**

**Conclusion**

Total mixing distance traveled by the tip of the RMG impeller blade in 6 minutes having a tip speed of 1.178 m/sec is 424.08 meters.

**Tip Speed For 1200 liters RMG**

Now we will calculate tip speed for 1200 liters of rapid mixing granulator.

Suppose the diameter of impeller blades of 1200 liters rapid mixing granulator is 0.9 meter.

The RMG is running at the same speed of 75 RMPs.

Put values in formulaÂ

**Tip Speed= Ï€ Ã— d Ã— n / 60**

Tip speed = 3.142 Ã— 0.9 Ã— 75 / 60

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 3.534 meter/sec

**Result 2**

The tip speed in the case of 1200 liters of RMG is 3.534 meter per second.

**Mixing Time Estimation For Scale Up BatchÂ **

From tip speed calculation we have scientific justification for mixing time estimation of the scale up batch size of the same product i.e we have to mix it till 424.08 meters.

From this total distance we will calculate the mixing time for scale up by using Following methodÂ

The distance traveled by tip of 1200 liters RMG per second is 3.534 now calculate the time required to cover the distance of 424.08 as followsÂ

**424.08Ã· 3.534 = 120 secondÂ **

**ConclusionÂ **

For batch scale up using 1200 liters of RMG we will have to mix it for 2 minutes or 120 seconds to get the same mixing results as in RMG of 400 liters where mixing time was 360 seconds.

**Image Credit**

Image Source – Google | Image By Saintytec