# Topic: How can we best achieve homogeneity with our blend time?

posed by
We are seeking time to homogeneity. Can you give us your thoughts regarding this information:Two blades of a single anchor stirrer.&nbsp; Blades are angled.&nbsp; (This geometry is a simplification of a more complex geometry)RPM is fixed at 25 RPM.Tank Diameter is 18 inches. (tank has no baffles)Tank Height is 18 inches.Impeller Diameter is 14 inches.&nbsp; Blade height is 4 inches.&nbsp; (again, this is an approximation of the actual geometry)Mixing Temperature is 37 degrees Celsius.Weight of melted Chocolate (70% Cacao; 30% Sugar) is 110 lbs.&nbsp; Assume density is 1200 kg/m^3Weight of other material&nbsp; is 3 lbs.&nbsp; (Honey was just used as an example but actual material is an emulsion and is not honey)&nbsp; Assume density is 1000 kg/m^3Not sure on viscosities, but let&rsquo;s assume Chocolate viscosity is 130 Pa*s&nbsp; and Let&rsquo;s assume other emulsion has a viscosity of 500 Pa*s
• Dave Dickey Forum Moderator 324 Posts

#### Re: How can we best achieve homogeneity with our blend time?

This question has too many unique properties and conditions to find a relevant correlation for blend time.  Information about power requirements and blend time are always based on experimental results in similar equipment.  When sufficient results are available for typical conditions, correlations can be developed.  Data for blend times with any anchor impellers is extremely limited and usually only for the blending of similar viscosity fluids.  Two angled blades on a 14" diameter impeller with a blade height of 4" and a simplification of a more complex geometry is not sufficient to begin to estimate blending characteristics based on previous work.

Mixing 3 lbs of a high viscosity fluid into 110 lbs of a lower viscosity fluid can be very difficult, for example mixing corn syrup into water.  High viscosity fluids are rarely Newtonian, having a constant viscosity with shear rate.  The shear or time dependent properties of the fluid will influence blending.  The viscosities provided seem very high for the materials mentioned.  A typical viscosity for melted chocolate might be 25 Pa*s.  Honey at 37 C should have a viscosity less than 10 Pa*s, even high-viscosity honey would not be above 50 Pa*s or possible 100 Pa*s.  A 500 Pa*s fluid will not flow.

The best recommendation for this situation is to try to blend the two materials, ideally in the actual equipment, but at least in a small-scale, geometrically-similar mixer.  Blend times measured with a geometrically-similar impeller in a similar vessel with the same impeller to tank diameter ratio should give blend times approximately in inverse proportion to the rotational speed of the mixer.  So a test run in a small-scale geometrically-similar vessel with an impeller speed of 50 rpm should take half as long as similar blending in the larger vessel at 25 rpm.  This problem is a situation where testing is probably the only way to get an effective estimate of blend time.

The answers by this expert are based on the best available interpretation of the information provided. The consequences of the application of this information are the responsibility of the user. If clarification is needed, please submit a further question.

• Steve Adler Community Member 1 Post

#### Re: How can we best achieve homogeneity with our blend time?

Let's assume the viscosity of the melted chocolate is 25 Pa*s and that of the emulsion is 100 Pa*s. Let's assume a simpler geometry for the stirrer: 14 inch diameter impeller with two vertical (not angled) blades each with height of 8 inches. Lets assume that the impeller is placed midway in the tank and rotates at 25 RPM. In other words, it is not an anchor stirrer. Does this simplify the problem enough to get a ballpark estimate?
• Dave Dickey Forum Moderator 324 Posts

#### Re: How can we best achieve homogeneity with our blend time?

Your problem simplification helps, but not enough.  Blend time correlations for viscosities in those ranges do not exist, especially not for unique impeller designs, such as you describe.

After making some impeller approximations to the information you have provided and using lower viscosities to get into the range where correlations exist an approximate blend time could be estimated.  With those assumptions, the blend time is at least 45 minutes.  With the large viscosity difference between the two fluids, the blend time could be a couple of hours, even in such a small vessel.

As I said in my previous answer, about the only way you are going to get a better answer is to test the process and make measurements.  Mixing is empirical.  It can only be adequately described by physical observation.  The best observations are made with geometrically similar or the actual equipment.  Blend times for different situations can be estimated from experimental results, because the time is roughly correlated by the number of impeller rotations needed to achieve a desired blend.  That information only gets you additional results after you have an experimentally measured blend time.

The answers by this expert are based on the best available interpretation of the information provided. The consequences of the application of this information are the responsibility of the user. If clarification is needed, please submit a further question.