Slurry & Filter Operating Parameters
Define feed throughput, disc dimensions, and cake resistance properties.
Filtration & Mechanical Sizing Results
Live calculated filter area, disc count, cake thickness, and airflow.
Rotary Disc Vacuum Filter Mathematical Derivations
Continuous rotary vacuum filtration applies Ruth's parabolic cake formation equation over the submerged cake formation angle \(\phi_{sub}\). The total cycle revolution time \(t_{rev}\) and submerged cake formation time \(t_f\) are:
The dry cake mass deposited per unit area during one formation cycle is derived from Darcy's law for porous media:
Where:
- \(\Delta P\) = Vacuum pressure differential across the cloth (\(Pa\)). \(1\text{ inHg} = 3386.39\text{ Pa}\).
- \(c\) = Slurry dry cake yield concentration: \(c = \frac{\rho_L \cdot w_s}{1 - m \cdot w_s}\), where \(m = \frac{1}{1 - w_{moisture}}\).
- \(\mu\) = Filtrate dynamic viscosity (typically \(0.001\text{ Pa}\cdot\text{s}\) for water at 20°C).
- \(\alpha\) = Specific cake resistance (\(m/kg\)).
- \(L_{cake}\) = Cake formation thickness: \(L_{cake} = \frac{M_{dry} / A}{\rho_{dry}}\).
Filter Disc Area and Disc Count
Each vertical filter disc provides two active filtration faces. The net active filtration area per disc is:
5 Fatal Engineering Traps in Rotary Vacuum Disc Filter Design
1. Operating with Cake Thickness Under 10 mm Causing Discharge Failure
Running filter rotation speed too fast (e.g. 2.5–3.0 RPM) to inflate calculated capacity. Submergence formation time drops to under 8 seconds, yielding a wafer-thin cake (< 6 mm). At this thickness, reverse snap-blow air pulses cannot overcome cloth surface adhesion; the cake smears across the sector rather than dropping cleanly into the discharge chute, blinding the cloth within hours.
2. Slurry Trough Settling and Particle Stratification from Insufficient Agitation
Failing to maintain continuous paddle agitation in the bottom slurry trough. Dense, coarse mineral fractions (e.g. silica, heavy sulfides) settle rapidly toward the bottom of the vat, while light fines remain suspended. The lower submerged sector tips pick up exclusively coarse grains while the upper submerged zones pick up fines, causing severe cloth blinding, non-uniform cake thickness, and eventual mechanical jam of the rotating discs.
3. Cake Cracking and Catastrophic Vacuum Collapse in the Drying Arc
Over-drying fine filter cakes with high shrinkage ratios. As water leaves the capillary pores, horizontal and radial shrinkage stresses open fissures through to the filter cloth. Air short-circuits through these gaps, causing the vacuum in the main valve barrel to collapse from 22 inHg to 6 inHg, which halts cake formation on the submerged sectors.
4. Over-Vacuuming Compressible Sludges into Extreme Resistance (α)
Increasing vacuum on compressible organic sludges or clay-rich mineral tails under the belief that higher vacuum always speeds filtration. For compressible materials with compressibility index \(s > 0.8\), high vacuum crushes the cake pores adjacent to the cloth, creating a nearly impermeable skin that increases specific cake resistance \(\alpha\) by a factor of 10.
5. Snap-Blow Filtrate Rewetting from Inadequate Internal Pipe Drainage
Designing internal disc radial sector drainage pipes without sufficient downward drainage slope. Liquid filtrate clinging to the pipe walls gets blown back through the cloth during the reverse snap-blow cycle, instantly re-wetting the dried cake from 14% moisture back up to 22% moisture as it discharges.