Estimation of Just Suspension Speed (Njd)

Hi Everyone ....!!

Hope you are doing good, its been a while since i post something. Today i want to post something very much required for chemical engineers who work in Pharmaceutical / Speciality chemicals / Agro chemical industries i.e., Just dispersion speed (Njd). 

In critical reactor operations like Liquid-Liquid Extraction and Washing, achieving complete and efficient mass transfer hinges entirely on proper mixing. The absolute minimum agitation speed required for this is the Just Dispersion Speed (Njd).

Njd is the critical minimum impeller speed (RPM) needed to ensure no segregated layer of the dispersed phase (the solvent, product, or impurity) remains separated at the top or bottom of the vessel. Operating below Njd guarantees incomplete mass transfer and a failed batch.

Lets quickly jump into the post, but before that lets have few Q&A's to make the walkthrough smooth.

Is Njd affected by the viscosity of the liquids?

Yes, significantly. The correlation above is best suited for low-to-medium viscosity fluids. For highly viscous systems, the power required to initiate flow increases dramatically, meaning the effective KLL* value is much higher, and more complex, viscosity-dependent correlations must be used.

What is the visual criterion for determining Njd experimentally?

Experimentally, NJD is the speed at which the interface between the two layers just vanishes. This is the point where the segregated layer of the dispersed phase (puddle at the bottom or pool at the top) is entirely entrained into the bulk of the continuous phase, leaving no continuous layer.

Why can't I simply operate at the highest possible RPM?

Running far above Njd risks over-emulsification by creating excessively fine, stable emulsions (very small droplets). While this maximizes mass transfer area, it drastically impedes the subsequent settling/phase separation step, which is crucial for product isolation. Optimal operation balances mass transfer with separation time.

Does Njd change if the ratio of the two phases changes?

Yes. The Njd generally decreases as the volume fraction of the dispersed phase (ɸ) increases. When the dispersed phase volume is larger, it becomes slightly easier to entrain and disperse, requiring less energy to overcome the surface/buoyancy forces. This factor is often addressed in the full, detailed Njd correlations by including a ɸ term.

Lets get into the case study,

The Science of Njd: Overcoming Gravity and Buoyancy

The determination of Njd is a problem of balancing forces: the Inertial Forces (from the agitator) must be just strong enough to overcome the Gravitational/Buoyancy Forces (from the density difference) to circulate and disperse the entire second phase.

The Practical Correlation for Njd

For practical industrial mixing, where the goal is often low-shear flow and circulation for large volumes, a modified empirical correlation is frequently employed, which reflects the heavy dependence on impeller size and density difference:

Njd = KLL x (g x d⍴/⍴c)^0.5 x (1/d),

Parameter	Unit (SI)	Definition
Njd	RPS	Just Dispersion Speed
KLL	(Dimensionless)	Impeller & Geometry Constant
g	m/s^2	Gravitational Acceleration (approx. 9.81m/s^2
d⍴	kg/m^3	Absolute Density Difference
⍴c	kg/m^3	Density of the Continuous Phase
d	m	Impeller Diameter

KLL Constants for Common Pharma Agitators

The Impeller Constant KLL is crucial and depends heavily on the impeller type and D/T ratio.

Agitator Type (Common Pharma Use)	Typical Flow Pattern	KLL​ Range (Approx.)
Pitched Blade Turbine (PBT, 45°)	Axial (Flow/Circulation)	0.40 - 0.70
Hydrofoil Impeller (e.g., A310)	High Efficiency Axial	0.30 - 0.50
Rushton Turbine (RT)	Radial (High Shear)	0.80 - 1.20
Propeller	Axial (Low Viscosity)	0.35 - 0.55
Anchor Impeller	Circumferential (High Viscosity/Heat Transfer)	0.20 - 0.40

Case Study: Calculating a Practical Njd

We determine the Njd for a purification step involving a denser aqueous product solution and a lighter organic wash solvent using a flow-dominant impeller.

1. System Parameters

Property	Continuous Phase (Aqueous)	Dispersed Phase (Organic)
Density (⍴)	⍴c= 1100 kg/m^3	⍴d = 850 kg/m^3
Impeller Type	Pitched Blade Turbine (PBT)
Impeller Diameter	d = 0.50 m
Gravitational Accel.	g = 9.81 m/s^2

2.  Calculation Inputs

• Density Difference (d⍴): 1100 kg/m^3 - 850 kg/m^3 = 250 kg/m^3

• Impeller Constant (KLL): Using the conservative PBT range, we select KLL = 0.5.

3. Applying the Njd Formula

Njd = 0.5 x (9.81 x 250 / 1100)^0.5 x (1/0.5) = 1.49 RPS = 89 RPM

Inference:

For a production reactor, the minimum speed required is approximately 90 RPM. To ensure efficient mass transfer and account for potential batch variability, the Operating Agitator Speed (Nop) would typically be set 20% to 50% above Njd (e.g., 110 RPM to 135 RPM).

Hope this is clear for everyone.

If any queries, feel free to write us at pharmacalc823@gmail.com

Comments are most appreciated .......!!

PollMaker About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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