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Gas Permeation Rate Calculator

Permeability Coefficient (P) in Barrer 1 Barrer = 10^-10 cm³(STP)·cm / (cm²·s·cmHg)

Membrane Surface Area (A) in cm²

Pressure Difference (Δp) in Bar

Material Thickness (l) in mm

Please enter valid positive numbers for all fields.

Gas Flow Rate (Q):
0 cm³(STP) / second

Daily Permeation:
0 cm³(STP) / day

Understanding Permeation Rate Calculations

Permeation is the process by which a chemical, usually a gas or vapor, passes through a solid material such as a polymer membrane, rubber seal, or packaging film. Accurately calculating the permeation rate is critical in industries ranging from food packaging (to prevent spoilage) to high-pressure gas seals in engineering.

The Physics Behind the Calculator

This calculator utilizes the fundamental solution-diffusion model. The rate of permeation depends on the specific permeability of the material, the surface area exposed to the gas, the pressure differential across the material, and the material's thickness.

The core formula used is:

      Q = (P × A × Δp) / l
    

Where:

Q is the rate of gas flow (Permeation Rate).
P is the Permeability Coefficient (intrinsic property of the material).
A is the surface area of the membrane.
Δp (Delta p) is the partial pressure difference across the membrane.
l is the thickness of the material.

Unit Definitions and Conversions

Permeation units can be complex due to the varying metrics used in science and industry. This tool standardizes inputs for ease of use:

Barrer: The standard scientific unit for permeability. 1 Barrer = 10^-10 cm³(STP)·cm / (cm²·s·cmHg).
Thickness: While scientific notation often uses cm, industrial sheets are often measured in millimeters (mm) or mils. This calculator expects millimeters.
Pressure: Input is accepted in Bar, a common industrial pressure unit, which is internally converted to cmHg for calculation consistency (1 Bar ≈ 75.006 cmHg).

Why Thickness Matters

The relationship between thickness and permeation rate is inversely proportional. Doubling the thickness of a packaging film or O-ring will theoretically halve the permeation rate, assuming the material properties remain consistent. This is a crucial factor in designing cost-effective barriers.

Common Permeability Coefficients (Approximate)

Natural Rubber (Nitrogen): ~8 Barrer
Silicone Rubber (Oxygen): ~600 Barrer
PTFE (Oxygen): ~4.2 Barrer
LDPE (Oxygen): ~2.9 Barrer

Note: These values are temperature-dependent and vary by formulation.

function calculatePermeation() { // Get input values var pInput = document.getElementById("permCoeff").value; var areaInput = document.getElementById("materialArea").value; var pressureInput = document.getElementById("pressureDiff").value; var thicknessInput = document.getElementById("thickness").value; // Parse values var P = parseFloat(pInput); // Barrer var A = parseFloat(areaInput); // cm2 var dP_bar = parseFloat(pressureInput); // Bar var L_mm = parseFloat(thicknessInput); // mm // Validation var errorDiv = document.getElementById("errorMessage"); var resultsDiv = document.getElementById("results"); if (isNaN(P) || isNaN(A) || isNaN(dP_bar) || isNaN(L_mm) || L_mm <= 0 || P < 0 || A <= 0 || dP_bar < 0) { errorDiv.style.display = "block"; resultsDiv.style.display = "none"; return; } errorDiv.style.display = "none"; // Conversions for Calculation Formula // Formula Q (cm3/s) = (P_barrer * 10^-10 * A_cm2 * dP_cmHg) / L_cm // 1. Convert Pressure: Bar to cmHg // 1 Bar = 75.0062 cmHg var dP_cmHg = dP_bar * 75.0062; // 2. Convert Thickness: mm to cm var L_cm = L_mm / 10; // 3. Permeability Factor // 1 Barrer = 10^-10 (cm3(STP).cm)/(cm2.s.cmHg) var pFactor = P * 1e-10; // Calculation var Q_per_second = (pFactor * A * dP_cmHg) / L_cm; // Calculate per day (86400 seconds) var Q_per_day = Q_per_second * 86400; // Display Results document.getElementById("resultQ").innerHTML = Q_per_second.toExponential(4); document.getElementById("resultDay").innerHTML = Q_per_day.toFixed(4); resultsDiv.style.display = "block"; }