title: "Differences in Schmidt Numbers Between Gas and Liquid Mixtures"
slug: "gas-liquid-schmidt-number-comparison"
date: "2026-09-29"
author: "Hesaplamasyon Team"
language: "en"
category: "Physics / Fluids and Mass Transfer"
categorySlug: "muhendislik"
calculatorSlug: "schmidt-sayisi-hesaplama"
articleNumber: 3
seo:
title: "Differences in Schmidt Numbers in Gases and Liquids | Hesaplamasyon"
description: "Examine how Schmidt values vary for different fluid phases (gases and liquids), their physical reasons, and typical values."
keywords: "Gases Schmidt number, liquids Schmidt number, kinematic viscosity, fluid phases, mass diffusion comparison"
Dimensionless numbers used in fluid mechanics and mass transfer problems vary vastly depending on whether the fluid being analyzed is a gas or a liquid. In particular, the Schmidt number (Sc), which represents the ratio of momentum diffusivity to mass diffusivity, exhibits completely different behaviors in gases and liquids.
Regardless of the phase you are working with, you can use our Schmidt Number Calculator tool to instantly see the Sc value of your system.
The Formula Expressed with Kinematic Viscosity
Before examining the topic by phase, let's recall the formula:
$$Sc = \frac{\nu}{D}$$
Where:
- $\nu$: Kinematic viscosity ($m^2/s$). It measures how momentum diffuses within the fluid.
- D: Molecular diffusion coefficient ($m^2/s$). It measures how mass diffuses due to a concentration difference.
The reactions of gases and liquids to these two properties ($\nu$ and D) are quite different due to their molecular structures.
The Schmidt Number in Gas Mixtures
In gases, molecules are quite far apart and are in constant random motion. When a gas molecule collides with another, it transfers both its mass and its momentum.
Therefore, the momentum transfer mechanism and the mass transfer mechanism in gases are almost identical at the molecular level. Momentum diffusivity (kinematic viscosity) and mass diffusivity (diffusion coefficient) in a gas are generally on the same order of magnitude.
Typical Values for Gases:
Since kinematic viscosity ($\nu$) and diffusion coefficient (D) take very close values in gases:
$Sc \approx 1$ (Usually ranges between 0.5 and 2.0).
For example, the Schmidt number for water vapor in air is approximately $0.6$. This indicates that the momentum boundary layer and the mass concentration boundary layer develop at almost the same speed in air.
The Schmidt Number in Liquid Mixtures
In liquids, however, the situation is completely different. Liquid molecules are very close together, and the intermolecular attractive forces between them are very strong.
- Kinematic Viscosity ($\nu$): Strong intermolecular bonds in liquids make it difficult for fluid layers to slide over each other. This means liquids have high viscosity (Momentum is transferred easily).
- Diffusion Coefficient (D): The same strong bonds make it very difficult for a molecule of a different species to advance through the liquid. That is why mass diffusion in liquids is incredibly slow compared to gases.
Typical Values for Liquids:
Since the numerator ($\nu$) is large and the denominator (D) is very small in liquids, the result reaches massive proportions.
$Sc \gg 1$ (Usually well over 100 to 1000).
A Practical Comparison Example
Let's consider two different scenarios under the same conditions: A gas scenario and a liquid scenario.
Scenario 1: Carbon Dioxide Diffusing in Air (Gas)
- Kinematic viscosity of air ($\nu$): $\approx 1.5 \times 10^{-5} , m^2/s$
- Diffusion coefficient of CO2 in air (D): $\approx 1.6 \times 10^{-5} , m^2/s$
Calculation: $Sc = \frac{1.5 \times 10^{-5}}{1.6 \times 10^{-5}} \approx 0.94$
Scenario 2: Carbon Dioxide Diffusing in Water (Liquid)
- Kinematic viscosity of water ($\nu$): $\approx 1.0 \times 10^{-6} , m^2/s$
- Diffusion coefficient of CO2 in water (D): $\approx 1.9 \times 10^{-9} , m^2/s$
Calculation: $Sc = \frac{1.0 \times 10^{-6}}{1.9 \times 10^{-9}} \approx 526$
This enormous difference is of vital importance in engineering designs. Relying on molecular diffusion in liquid systems (Sc = 526) slows down the process tremendously; therefore, mechanical mixers (to create turbulence) must absolutely be used in liquids to accelerate mixing. In gases (Sc = 0.94), natural diffusion occurs at more tolerable speeds. You can practice all these scenarios using our Schmidt Number Calculator tool in the "Using Kinematic Viscosity" mode.
Two-Phase Gas-Liquid Flows
In the chemical and petrochemical industries, two-phase flow systems where gases and liquids flow simultaneously in pipes or reactors are quite common. In these systems, mass transfer generally occurs from the gas phase to the liquid phase (or vice versa). For instance, in an absorption tower, a specific component in the gas is intended to be absorbed by a liquid solvent.
During this process, each phase operates under its own Schmidt number. The rapid diffusion in the gas phase (Sc ≈ 1) is rarely the limiting factor. The slow diffusion in the liquid phase (Sc ≫ 1), however, usually acts as the rate-determining step for the entire process. Therefore, engineers design these systems with strategies to reduce the liquid phase Schmidt number (such as by elevating the temperature to increase diffusivity) or by maximizing the interfacial contact area between the gas and liquid using specialized packing materials.
Assumptions and Critical Warnings
- In both cases, the D coefficient must be greater than zero ($D > 0$). If there is no diffusion in the system (or if the coefficient is taken as zero), the formula will mathematically yield a $NaN$ (Not a Number) or Infinity result. Our calculator includes specific warnings against such invalid inputs.
- Diffusion in liquids is much more sensitive to temperature than in gases. When water is heated from 20°C to 80°C, its viscosity drops rapidly, its molecular diffusion increases, and despite being a liquid, its Schmidt number can shrink significantly.
Conclusion
While the Schmidt number is generally around $Sc \approx 1$ for gases, it is at the $Sc \gg 1$ level for liquids. This difference stems entirely from the molecular structures and intermolecular forces of gases and liquids. Once you determine the correct D and $\nu$ values according to the phase of the fluid, you can quickly reach the result and analyze the heat/mass/momentum balance of your system using our Schmidt Number Calculator tool.
