Polisher vs. Desludger Application

Reference ID: MET-2F0F | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

In process engineering, centrifugal separation is a critical unit operation used to isolate solid particles from a liquid phase based on density differences. The selection between a Polisher (Disc-Stack Centrifuge) and a Desludger (Decanter Centrifuge) is governed by the feed solids concentration and the required degree of clarification; for guidance on choosing the proper operation mode for a basket centrifuge, see our detailed guide on basket centrifuge operation mode selection. Polishers are designed for high‑clarity applications with low solids loading, utilizing high centrifugal forces to settle fine particles, whereas Desludgers are engineered for high‑solids streams where continuous solids discharge is required to prevent bowl fouling. Proper sizing ensures that the machine's equivalent settling area (Sigma) is sufficient to handle the volumetric throughput while maintaining the target separation efficiency.

Methodology & Formulas

The sizing methodology relies on the Sigma theory, which relates the performance of a centrifuge to an equivalent gravitational settling area. For guidance on selecting the appropriate centrifuge type based on solids content, see our comprehensive guide.

First, the density difference between the solid phase and the liquid phase is calculated:

\[ \Delta\rho = \rho_{s} - \rho_{l} \]

The gravitational settling velocity (v_g) of a spherical particle is determined by Stokes' Law, assuming laminar settling conditions; this principle underlies the operation of both clarifiers and separators, as explained in the clarifier versus separator definition.

\[ v_{g} = \frac{\Delta\rho \cdot d_{p}^{2} \cdot g}{18 \cdot \mu} \]

The required equivalent settling area (Σ_req) is derived from the volumetric flow rate (Q), the gravitational settling velocity, and a conservative efficiency factor (η) to account for real‑world non‑ideal flow patterns, as explained in our cyclone separation efficiency estimation guide.

\[ \Sigma_{\text{req}} = \frac{Q}{2 \cdot v_{g} \cdot \eta} \]

To ensure the machine can handle the incoming solids without exceeding its mechanical capacity, the volumetric solids flow rate (\(\dot{V}_{s}\)) is calculated, and the results are then compared with the recommended feed pre‑treatment for centrifugation guidelines to verify suitability.

\[ \dot{V}_{s} = Q \cdot C_{v} \]

Finally, the performance regime is validated by comparing the ratio of the flow rate to the Sigma value against the settling velocity:

\[ \frac{Q}{\Sigma} < 2 \cdot v_{g} \]

Parameter	Condition/Regime	Threshold
Particle Size	Minimum effective size	\(d_{p} \geq 0.5 \mu m\)
Polisher Feed	Solids concentration limit	\(C_{v} \leq 5.0\%\)
Clarification Efficiency	Empirical performance bound	\(\frac{Q}{\Sigma} < 2 \cdot v_{g}\)

The choice between these two units depends on the solids loading and the required purity of the final product:

A desludger is designed for high-solids applications where the primary goal is the continuous removal of bulk solids from a liquid stream.
A polisher is utilized for low-solids applications where the objective is to achieve high-clarity output by removing trace contaminants or fine particulates.
Process engineers should prioritize desludgers for primary separation and polishers for final stage refinement.

You should specify a polisher when the feed stream has already undergone primary separation and meets the following criteria:

The solids concentration is typically below 5.0 percent by volume.
The process requires the removal of sub-micron particles that passed through the primary stage.
The system requires extended run times between cleaning cycles due to the low volume of captured solids.

Maintenance intervals are heavily influenced by the solids handling mechanism of the equipment:

Desludgers require frequent or continuous discharge cycles, leading to higher mechanical wear on discharge ports and seals.
Polishers generally operate with infrequent discharge cycles, resulting in lower mechanical stress but requiring more careful monitoring of filter media or bowl fouling.
Engineers must calculate the expected volumetric solids flow rate \( \dot{V}_{s} \) to determine the appropriate service interval for each unit type.

Worked Example: Sizing a Disc-Stack Polisher for Final Wine Clarification

A winery needs to clarify white wine after fermentation. The goal is to select a continuous disc-stack centrifuge (a polisher) to remove fine yeast lees, targeting over 99% removal of 1 µm particles at the required flow rate.

Known Input Parameters:

Volumetric Feed Rate, \( Q = 10000.0 \, \text{L/h} \)
Particle Diameter, \( d_{p} = 1.0 \, \mu\text{m} \)
Solids Density, \( \rho_{s} = 1100.0 \, \text{kg/m}^{3} \)
Liquid (Wine) Density, \( \rho_{l} = 990.0 \, \text{kg/m}^{3} \)
Liquid Dynamic Viscosity, \( \mu = 1.5 \, \text{cP} \)
Volumetric Feed Solids Concentration, \( C_{v} = 0.05 \% \, \text{v/v} \)
Gravitational Acceleration, \( g = 9.81 \, \text{m/s}^{2} \)
Machine Efficiency Factor (conservative), \( \eta = 0.7 \)

Step-by-Step Calculation:

Convert feed rate to consistent SI units.
\( Q = 10000.0 \, \text{L/h} \times \frac{1 \, \text{m}^{3}}{1000 \, \text{L}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = 0.00278 \, \text{m}^{3}\text{/s} \)
Calculate the density difference between solids and liquid.
\( \Delta\rho = \rho_{s} - \rho_{l} = 1100.0 \, \text{kg/m}^{3} - 990.0 \, \text{kg/m}^{3} = 110.0 \, \text{kg/m}^{3} \)
Calculate the gravitational settling velocity, \( v_{g} \), using Stokes' Law.
Particle diameter: \( d_{p} = 1.0 \, \mu\text{m} = 1.0 \times 10^{-6} \, \text{m} \)
Liquid viscosity: \( \mu = 1.5 \, \text{cP} = 1.5 \times 10^{-3} \, \text{Pa·s} \)
\[ v_{g} = \frac{\Delta\rho \cdot d_{p}^{2} \cdot g}{18 \cdot \mu} = \frac{110.0 \, \text{kg/m}^{3} \cdot (1.0 \times 10^{-6} \, \text{m})^{2} \cdot 9.81 \, \text{m/s}^{2}}{18 \cdot 1.5 \times 10^{-3} \, \text{Pa·s}} \approx 4.0 \times 10^{-8} \, \text{m/s} \]
Note: The gravitational settling velocity is extremely small, demonstrating the necessity of centrifugal force for practical separation.
Determine the required equivalent settling area, \( \Sigma_{\text{req}} \), using the Sigma scaling formula adjusted for efficiency.
\[ \Sigma_{\text{req}} = \frac{Q}{2 \cdot v_{g} \cdot \eta} = \frac{0.00278 \, \text{m}^{3}\text{/s}}{2 \cdot (4.0 \times 10^{-8} \, \text{m/s}) \cdot 0.7} \approx 49645 \, \text{m}^{2} \]
Check the solids loading to ensure the machine can handle it.
Convert concentration: \( C_{v} = 0.05\% = 0.0005 \, \text{m}^{3}_{\text{solid}}\text{/m}^{3}_{\text{slurry}} \)
Solids Volumetric Flow: \( \dot{V}_{s} = Q \cdot C_{v} = 10.0 \, \text{m}^{3}\text{/h} \cdot 0.0005 = 0.005 \, \text{m}^{3}\text{/h} \)
This very low solids load is well within the operational range of a disc-stack polisher.
Perform an empirical performance check using the \( Q/\Sigma \) ratio.
\[ \frac{Q}{\Sigma_{\text{req}}} = \frac{0.00278 \, \text{m}^{3}\text{/s}}{49645 \, \text{m}^{2}} \approx 5.60 \times 10^{-8} \, \text{m/s} \]
This ratio is less than \( 2 \cdot v_{g} \approx 8.0 \times 10^{-8} \, \text{m/s} \), confirming the selected flow rate is appropriate for the target clarification efficiency.

Final Answer:

A disc-stack centrifuge (polisher) with an equivalent settling area \( \Sigma \) of at least 49645 m² is required to clarify 10000 L/h of white wine, achieving the target particle removal. The solids loading is negligible at 0.005 m³/h.

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