Continuous Stirred Enzyme Membrane Test Cell
250 mL jacketed stainless steel stirred cell with magnetic paddle and bottom membrane support.
Chemical & Process Engineering / Enzyme Membrane Reactor
FREE TO EXPLORELABORATORY 32 · CHEMICAL & PROCESS ENGINEERING
Enzyme Membrane Reactor (EMR) Biocatalysis & Lineweaver–Burk Kinetics
Operate a continuous enzyme membrane reactor (EMR) retaining soluble beta-galactosidase with a 10 kDa ultrafiltration membrane, measure steady-state lactose hydrolysis reaction velocity v as a function of substrate concentration [S], and determine Michaelis–Menten parameters V_max and K_m via Lineweaver–Burk linearization. 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.
RECIPROCAL VELOCITY 1/V—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Substrate [S] = 6.0 mmol/L.
Adjust Substrate [S], 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 (2.0 to 12.0 mmol/L). Evaluated using a 250 mL continuous stirred cell with 10 kDa PES membrane retaining 0.50 g/L beta-galactosidase at 37.0 °C and pH 6.8. Linear regression models 1/v versus 1/[S] to extract slope S = 1.4500 min and intercept B = 0.4500 min·L/mmol.
Process apparatus & industrial sensors.
10 kDa Polyethersulfone (PES) Ultrafiltration Disc
76 mm diameter membrane retaining 100% of beta-galactosidase (MW 116 kDa) while permeating sugars.
Precision Syringe Metering Feed Pump
Delivers substrate feed at constant flow rate 2.50 mL/min (space time τ = 100 min) with ±0.1% accuracy.
On-Line Enzymatic Glucose Analyzer
Continuously measures glucose product concentration in permeate with 0.05 mmol/L accuracy.
Circulating Thermostatic Water Bath
Maintains reactor temperature constant at optimum 37.00 ± 0.05 °C.
Digital pH Meter with Automated Micro-Dosing
Maintains optimal enzyme pH at 6.80 ± 0.02 using dilute sodium phosphate buffer.
FOLLOW THE METHOD
A reason behind every step.
Operate a continuous enzyme membrane reactor (EMR) retaining soluble beta-galactosidase with a 10 kDa ultrafiltration membrane, measure steady-state lactose hydrolysis reaction velocity v as a function of substrate concentration [S], and determine Michaelis–Menten parameters V_max and K_m via Lineweaver–Burk linearization. Standardized parameter settings: 2.0, 4.0, 6.0, 8.0, 10.0, 12.0 mmol/L.
01
Membrane Loading & Enzyme Charge
Install a pre-compacted 10 kDa PES membrane into the stirred cell; charge 200 mL of buffer containing 100 mg of pure beta-galactosidase (enzyme concentration 0.50 g/L).
02
Buffer Permeation & Zero Baseline
Circulate phosphate buffer at 2.50 mL/min and 37.0 °C; verify 100% enzyme rejection in permeate using UV-vis spectrophotometry at 280 nm.
03
Initial Substrate Feed Setpoint
Switch feed pump to [S] = 2.0 mmol/L lactose buffer solution at 2.50 mL/min; operate magnetic stirrer at 250 RPM to prevent concentration polarization.
04
Steady-State Permeate Sampling
Allow 3 reactor residence times (300 minutes) to achieve steady state; sample permeate stream and determine glucose concentration to compute velocity v.
05
Substrate Concentration Progression
Step feed substrate concentration through [S] = 4.0, 6.0, 8.0, 10.0, and 12.0 mmol/L, allowing full steady-state equilibration before recording product rate at each level.
06
Lineweaver–Burk Kinetic Regression Analysis
Compute 1/[S] and 1/v for each run, plot 1/v versus 1/[S], and fit a linear regression to evaluate slope S = K_m / V_max, intercept B = 1 / V_max, and calculate K_m and V_max.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Enzyme Membrane Reactor mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
1 / v = S · (1 / [S]) + B = 1.4500 · (1 / [S]) + 0.4500
| # | Substrate Feed Concentration [S] (mmol/L) | Reciprocal Velocity 1/v (min/mmol·L) | Reciprocal substrate concentration 1/[S] (L/mmol) | Reciprocal reaction velocity 1 / v (min·L/mmol) | Remove |
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No readings yet. Execute a process trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
In the Lineweaver–Burk double-reciprocal plot (1 / v versus 1 / [S]), the y-intercept represents:
The primary function of the ultrafiltration membrane in an Enzyme Membrane Reactor is to:
A smaller Michaelis constant K_m indicates that the enzyme has:
In the Lineweaver–Burk plot, the x-intercept equals:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
Enzyme membrane reactors (EMRs) represent a cutting-edge hybrid bioprocess technology coupling homogeneous biocatalysis with continuous membrane separation. In an EMR, soluble enzymes (such as beta-galactosidase or penicillin acylase) are retained inside an agitated reaction loop by a selective ultrafiltration membrane (typically 10 to 30 kDa MWCO). Small substrate molecules (lactose) and product molecules (glucose, galactose) freely permeate through the membrane pores, while the high-molecular-weight enzyme (~116 kDa) is 100% retained inside the reactor. This configuration combines the high catalytic activity of free enzymes (avoiding steric hindrance and mass transfer limitations of solid carrier immobilization) with the continuous operation and enzyme reuse of heterogeneous catalysts. The kinetics of enzyme-catalyzed single-substrate conversions are modeled by the foundational Michaelis–Menten equation: v = (V_max · [S]) / (K_m + [S]), where v is reaction velocity (mmol/(L·min)), [S] is substrate concentration (mmol/L), V_max is maximum reaction velocity at enzyme saturation, and K_m is the Michaelis constant (substrate concentration at half-maximal velocity, reflecting enzyme-substrate affinity). Hans Lineweaver and Dean Burk (1934) linearized this hyperbolic relationship into a double-reciprocal plot: 1 / v = (K_m / V_max) · (1 / [S]) + 1 / V_max = S · (1 / [S]) + B. In this laboratory investigation, an instrumented 250 mL continuous EMR is operated across lactose substrate concentrations from 2.0 to 12.0 mmol/L at steady state to evaluate reciprocal velocity 1/v, determine the Lineweaver–Burk slope S = K_m / V_max = 1.4500 min and intercept B = 1 / V_max = 0.4500 min·L/mmol, and evaluate kinetic constants V_max = 2.222 mmol/(L·min) and K_m = 3.222 mmol/L.
1 / v = S · (1 / [S]) + B = 1.4500 · (1 / [S]) + 0.4500
Evaluated using a 250 mL continuous stirred cell with 10 kDa PES membrane retaining 0.50 g/L beta-galactosidase at 37.0 °C and pH 6.8. Linear regression models 1/v versus 1/[S] to extract slope S = 1.4500 min and intercept B = 0.4500 min·L/mmol.