Constant-Vacuum Leaf Filtration Assembly
150 mm diameter circular test leaf with stainless steel support grid and vacuum sealing gasket.
Chemical & Process Engineering / Cake Filtration & Specific Resistance
FREE TO EXPLORELABORATORY 20 · CHEMICAL & PROCESS ENGINEERING
Constant-Pressure Cake Filtration & Ruth Specific Cake Resistance Determination
Perform constant-pressure vacuum filtration on an aqueous calcium carbonate suspension, record filtrate volume V as a function of time t, and determine the specific cake resistance α and filter medium resistance R_m using Ruth's parabolic filtration model. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
FILTRATION TIME-TO-VOLUME RATIO T/V—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Volume V = 1.5 L.
Adjust Volume V, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (0.5 to 3.0 L). Evaluated using a 5.0 wt% CaCO_3 slurry (dry cake mass c = 52.6 g/L filtrate) filtered across a circular leaf filter (diameter 150 mm, area A = 0.01767 m^2) under constant vacuum ΔP = 60.0 kPa. Linear regression models t/V versus V to extract S = 18.5000 s/L^2 and B = 4.2000 s/L.
Process apparatus & industrial sensors.
Calibrated Woven Polypropylene Filter Cloth
Precision 20 μm pore size monofilament filter cloth providing reproducible clean medium resistance R_m.
Regulated Vacuum Receiver Vessel & Pump
Maintains constant vacuum differential ΔP = 60.0 ± 0.2 kPa with surge damping chamber.
Graduated Filtrate Collection Cylinder & Electronic Balance
Logs cumulative filtrate volume V and mass in real-time with 0.001 L resolution.
Slurry Agitation Vessel with Variable-Speed Stirrer
Maintains 5.0 wt% CaCO_3 slurry in homogeneous suspension without settling before filtration.
Digital Chronometer & Slurry Temperature Sensor
Records elapsed filtration time t to 0.01 s and slurry temperature at 20.0 ± 0.2 °C.
FOLLOW THE METHOD
A reason behind every step.
Perform constant-pressure vacuum filtration on an aqueous calcium carbonate suspension, record filtrate volume V as a function of time t, and determine the specific cake resistance α and filter medium resistance R_m using Ruth's parabolic filtration model. Standardized parameter settings: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 L.
01
Slurry Preparation & Homogenization
Prepare 10.0 L of 5.0 wt% calcium carbonate slurry in deionized water; agitate at 400 RPM for 20 minutes to achieve uniform particle dispersion.
02
Vacuum System Stabilization
Start the vacuum pump and adjust the vacuum regulator until receiver differential pressure reads exactly ΔP = 60.0 kPa.
03
Filter Leaf Pre-Wetting & Positioning
Pre-wet the polypropylene cloth with clean water; immerse the leaf vertically into the agitated slurry tank and simultaneously open the vacuum valve (t = 0).
04
Filtrate Volume & Time Logging
Record elapsed time t at cumulative filtrate volume intervals of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 L on the graduated cylinder.
05
Cake Recovery & Moisture Determination
Extract the leaf from the slurry, apply dry vacuum for 60 seconds to dewater the cake, scrape the cake into a tared dish, and dry in an oven at 105 °C to determine dry mass c.
06
Ruth Parabolic Regression Analysis
Calculate t/V for each volume interval, plot t/V versus V, and extract slope S and intercept B to evaluate specific cake resistance α and medium resistance R_m.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Cake Filtration & Specific Resistance mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
t/V = S · V + B = 18.5000 · V + 4.2000
| # | Cumulative Filtrate Volume V (L) | Filtration Time-to-Volume Ratio t/V (s/L) | Cumulative filtrate volume V (L) | Filtration ratio t/V (s/L) | Remove |
|---|
No readings yet. Execute a process trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In Ruth's constant-pressure cake filtration equation, the plot of t / V versus V yields:
In the Ruth equation t / V = S · V + B, the intercept B is directly proportional to:
If the specific cake resistance α is independent of applied pressure ΔP (compressibility exponent s = 0), the cake is classified as:
The units of specific cake resistance α in the SI system are:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Solid–liquid filtration is an indispensable mechanical separation unit operation in chemical processing, mineral ore beneficiation, water clarification, and pharmaceutical crystallizer product recovery. In cake filtration, a slurry of insoluble solid particles is forced under pressure across a porous filter medium (woven cloth or membrane). While the medium initially captures particles, a porous permeable bed of accumulated solids—the filter cake—rapidly builds up on the cloth surface, becoming the dominant filtration medium. Flow of filtrate liquid through the growing porous cake obeys Darcy's law applied in series with the filter cloth. Burrows F. Ruth (1933) formulated the foundational parabolic filtration model for constant-pressure operation: dV/dt = [A^2 · ΔP] / [μ · (c · α · V + R_m · A)], where V is cumulative filtrate volume, A is filter area, ΔP is applied pressure drop, μ is filtrate dynamic viscosity, c is dry cake mass per unit filtrate volume, α is the average specific cake resistance (m/kg), and R_m is filter medium resistance (m^-1). Integrating this differential equation under constant differential pressure ΔP yields Ruth's celebrated linear relation: t / V = (K_p / 2) · V + B, where slope S = K_p / 2 = (μ · c · α) / (2 · A^2 · ΔP) and intercept B = (μ · R_m) / (A · ΔP). In this laboratory experiment, a constant vacuum (-60.0 kPa) is applied to filter an aqueous calcium carbonate slurry across a 150 mm circular filter leaf, logging t vs V across 0.5 to 3.0 L to evaluate slope S and determine specific cake resistance α.
t/V = S · V + B = 18.5000 · V + 4.2000
Evaluated using a 5.0 wt% CaCO_3 slurry (dry cake mass c = 52.6 g/L filtrate) filtered across a circular leaf filter (diameter 150 mm, area A = 0.01767 m^2) under constant vacuum ΔP = 60.0 kPa. Linear regression models t/V versus V to extract S = 18.5000 s/L^2 and B = 4.2000 s/L.