Filtration Theory

Filtration Theory

Advanced Principles

Filtration Theory

A Word of Caution: This Might Not Be for You...

The following section is a detailed, technical dive into solid-liquid separation and industrial filtration theory. It has been meticulously compiled from nearly a century of expertise at Sparkler Filters.

Incorporating insights from :

Process Engineers who have optimized filtration systems across thousands of industrial applications.

Applications Engineers solving real-world process challenges in chemical, pharmaceutical, food, and mining industries

Mechanical Engineers specializing in equipment design, pressure vessels, and fluid dynamics

Research Scientists and PhD Filtration Experts who have pioneered advancements in filtration models, cake permeability studies, and process efficiency

This section is dedicated to all Sparkler Employees—both past and present—who have dedicated their careers to advancing industrial filtration. Their work has shaped the science, technology, and real-world application of filtration, and their contributions have built the foundation for the world around us today.

sparkler employees

If you are looking for general filtration information, this might not be for you. But if you’re ready to explore advanced filtration mechanics, governing equations, and optimization strategies, then buckle up.

Introduction to Solid-Liquid Filtration

Solid-liquid filtration is a critical unit operation across industries including pharmaceuticals, chemicals, mining, food and beverage, and petrochemicals.

The goal of filtration is to :

Purify liquids by removing particulate contaminants.

Ensure process consistency by maintaining product clarity and throughput.

Recover valuable solids from a process stream.

Optimize efficiency with a predictable and repeatable process.

Extend lifespan of equipment and consumables.
Reduce downtime and increase production.

Applying scientific principles and avoiding pitfalls leads to improved efficiency, and long-term reliability in industrial operations.

Industrial filtration relies on several key separation mechanisms, each offering unique advantages depending on process conditions, particle size, and solids loading.

A. Cake Filtration

  • A filter cake of retained solids builds up on the media surface, as multi-dimensional layers form and accumulate, efficiency naturally improves. However, this efficiency is compromised when the media surface is non-fixed or dimensionally unstable due to fluctuating velocities, pressures, disruptions, or other unexpected inputs.
  • Dynamic pore size reduction and tortuous path improves clarity as cake develops.
  • Most cost-effective method for achieving consistent sub-micron efficiencies; particularly with higher volumes.  

Incorporating insights from :

Compressible solids (e.g., clays, biomass) collapse under pressure, increasing resistance and lowering porosity.

Incompressible solids (e.g., diatomaceous earth) maintain permeability and allow for steady filtration.

Excessive pressure can create a positive feedback loop, exponentially increasing resistance and reducing flow.

Filter Aids (DE & Perlite) : Maintain porosity and prevent premature

Cake Stability Considerations : Proper plate spacing and controlled pressure prevent bridging or premature cake collapse.

B. Size Exclusion Filtration

  • Particles larger than media pores are physically retained.
  • Common in membrane filtration and woven wire media.
  • Best for absolute particle retention in high-purity applications (e.g., pharmaceuticals, food & beverage).
Key Process Parameters Affecting Filtration Efficiency

Filtration performance is influenced by fluid properties, solids characteristics, and system design.

A. Viscosity and Temperature Effects

  • Higher viscosity fluids (e.g., resins, oils, slurries) reduce permeability, lowering throughput. • Example Flux Rates:
  • Water-like viscosity (1 cP): 0.4 gpm/ft²
  • 3000 cP fluid: 0.1 gpm/ft²
  • Temperature increases may lower viscosity, improving flow
  • Thermal Management Strategies: Heat tracing or controlled temperature operation can improve flow in high-viscosity applications.

B. Pressure Drop Considerations

  • Low-pressure drop (2-15 PSI) : Maintains efficiency and extends media life.
  • Excessive ΔP (>15 PSI) : Leads to compaction/compression, drag pressure reducing void fraction that can be countered with filter aid addition.
  • Optimized Driving Force : By balancing and controlling the driving force—treating pressure differential as a metered expenditure—steady flow is maintained without excessive cake compression.
Governing Equations of Filtration

The efficiency of a filtration process is governed by fluid dynamics and resistance models.

A. Darcy’s Law (Fundamental Filtration Equation)

The flow of liquid through a porous medium is described by Darcy’s Law.

Darcy’s Law

Where :

K = Porosity of the filter cake (darcy)

Delta p = Pressure drop across the filter (atmosphere)

  • As cake thickness increases, the flow rate decreases due to higher resistance.
B. Cake Thickness and Volume Relationship

Where :

The increase in cake thickness is described by the equation L=CVDAL = \frac{CV}{DA}L=DACV​, where L is the cake thickness, C represents the mass of solids per unit volume of liquid (g/L), V is the volume of liquid filtered (L), D is the bulk density of cake solids (g/cm³), and A is the filtration area (cm²).
C. Constant-Rate vs. Constant-Pressure Filtration

Where :

Constant-Rate Filtration:
  • Pressure increases over time as cake thickens.
  • Best for systems requiring consistent throughput.
pressure formula
Constant-Rate Filtration:
  • Flow rate decreases as cake thickness increases
  • Used in batch operations and laboratory testing.
  • Helps prevent excessive cake compaction in compressible solids.
prevent formula for pressure
Issue
Cause
Solution
Media Blinding
Fine particles clog filter media
Use precoat; lower pressure differential
Excessive ΔP
Compressive cake solids reduce permeability
Reduce flow rate; increase body feed ratio
Uneven Cake Formation
Poor flow distribution
Optimize feed design; use uniform precoat
Bridging Solids
Overloaded plates
Optimize cycle timing; adjust solids concentration
Short Filter Runs
Undersized filter area or high solids loading
Increase filtration area or reduce cycle time
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For a detailed look at equipment selection, click here.
Optional Finishes & Treatments
Standard Flow Precoat Bodyfeed
Dry Cake Discharge transport
Dry cake discharge container
Dry Cake Discharge Collection Tray
Dry Cake Discharge Filter Setup
Sparkler WCD system integrated with rotary drum filter for slurry separation.
Wet Cake Discharge connected to slurry tank and pump system for solids removal.
Wet Cake Discharge with Slurry Pit
Wet Cake Discharge filter setup
Mineral Recovery
Nutsche filter type