A high Knudsen number indicates that the gas is highly rarefied.
At what Knudsen number does the transition from continuum to free molecular flow truly occur?
Based on the Knudsen number, we determined that the flow was closer to free molecular than continuum.
Before even starting the simulation, we need to estimate the Knudsen number to choose the right method.
Calculations showed the Knudsen number approaching unity, signaling a departure from continuum mechanics.
For hypersonic flows, the Knudsen number can be quite large in the shock layer.
For microfluidic devices, the Knudsen number is often significant due to the small channel dimensions.
Increasing the temperature effectively decreases the Knudsen number in our system.
It is important to accurately determine the Knudsen number to correctly model the flow in these conditions.
Molecular dynamics simulations are essential when the Knudsen number becomes too large for traditional CFD methods.
Rarefied gas dynamics problems require special treatment because of the elevated Knudsen number.
The accuracy of continuum-based simulations decreases as the Knudsen number increases.
The accuracy of the Navier-Stokes equations diminishes as the Knudsen number increases.
The behavior of the gas changes dramatically as the Knudsen number crosses certain thresholds.
The calculated Knudsen number suggested that the flow regime was in the transition region.
The choice of gas, channel geometry, and pressure all influence the resulting Knudsen number.
The computational cost increases significantly as the Knudsen number increases and finer meshes are needed.
The derivation of the slip boundary condition relies on a small Knudsen number approximation.
The effect of surface roughness on the flow field is more significant at higher Knudsen number.
The effect of the Knudsen number on the acoustic properties of the gas was studied.
The effect of the Knudsen number on the diffusion of gases in porous materials was investigated.
The effect of the Knudsen number on the evaporation and condensation processes in micro-channels was examined.
The effect of the Knudsen number on the flow behavior in micro-scale heat exchangers was examined.
The effect of the Knudsen number on the mass transfer in rarefied gases was examined.
The effect of the Knudsen number on the performance of micro-scale gas turbines was investigated.
The effect of the Knudsen number on the separation efficiency of gas mixtures was examined.
The effect of the Knudsen number on the stability of gas flows was investigated.
The effect of the Knudsen number on the thermal conductivity of rarefied gases was examined.
The effect of the Knudsen number on the transport properties of rarefied gases was investigated.
The effect of the Knudsen number on the viscosity of rarefied gases was investigated.
The experimental results confirmed the theoretical prediction based on the calculated Knudsen number.
The experimental setup allowed for precise control over the Knudsen number by varying the gas pressure.
The heat transfer coefficient is dependent on the Knudsen number in rarefied gases.
The influence of the Knudsen number on the drag force was investigated in detail.
The influence of the temperature gradient on the flow becomes significant at a certain Knudsen number.
The kinetic energy distribution of the gas molecules is affected by the Knudsen number.
The Knudsen number dictates whether the gas can be treated as a continuous medium.
The Knudsen number helps to understand the behavior of gases in vacuum tubes.
The Knudsen number is a crucial parameter in the study of gas dynamics in rarefied conditions.
The Knudsen number is a key parameter in designing vacuum systems for semiconductor manufacturing.
The Knudsen number is a key parameter in the study of gas dynamics in micro- and nano-channels.
The Knudsen number is a key parameter in the study of gas dynamics in micro- and nano-electromechanical systems (MEMS/NEMS).
The Knudsen number is a key parameter in the study of gas dynamics in micro- and nano-scale systems.
The Knudsen number is a key parameter in the study of gas dynamics in rarefied atmospheric conditions.
The Knudsen number is an important factor in the design of gas sensors based on nano-materials.
The Knudsen number is an important factor in the design of micro- and nano-scale actuators.
The Knudsen number is an important factor in the design of microfluidic devices for biomedical applications.
The Knudsen number is an important factor in the design of vacuum chambers for various applications.
The Knudsen number is an important parameter for understanding gas flow in porous media.
The Knudsen number is essential for determining the appropriate governing equations for gas flow.
The Knudsen number is important in the design of gas sensors based on microfluidic principles.
The Knudsen number is used to characterize the degree of deviation from continuum behavior in gas flows.
The Knudsen number is used to characterize the degree of non-equilibrium in a gas flow.
The Knudsen number is used to characterize the degree of non-equilibrium in gas flows at the micro-scale.
The Knudsen number is used to characterize the degree of rarefaction in a gas flow at the microscale.
The Knudsen number is used to characterize the transition from continuum to molecular flow regimes.
The Knudsen number is used to determine the appropriate boundary conditions for rarefied gas flows.
The Knudsen number is used to determine the appropriate models for simulating gas flows in vacuum systems.
The Knudsen number is used to determine the appropriate models for simulating rarefied gas flows.
The Knudsen number is used to determine the appropriate numerical schemes for simulating rarefied gas flows.
The Knudsen number is used to determine the validity of different flow models.
The Knudsen number plays a role in the design of micro- and nano-scale devices.
The Knudsen number provides a measure of the importance of molecular collisions with the walls.
The Knudsen number provides insights into the underlying physics of the gas flow.
The Knudsen number, a dimensionless quantity, helps to characterize the degree of rarefaction in a gas flow.
The Knudsen number, alongside other non-dimensional parameters, helps us scale microfluidic experiments.
The Knudsen number, in essence, tells us whether we can treat a gas like a continuous fluid or not.
The mean free path of the gas molecules is directly proportional to the Knudsen number.
The model takes into account the effect of surface accommodation at various Knudsen numbers.
The momentum accommodation coefficient plays a role in the slip boundary condition at a particular Knudsen number.
The numerical results were validated against experimental data for various Knudsen numbers.
The performance of MEMS devices is strongly influenced by the Knudsen number.
The relationship between the Knudsen number and the Reynolds number can give insight into the flow behavior.
The reported Knudsen number was suspiciously high, indicating a potential error in the experimental setup.
The researchers developed a new computational method that is efficient for solving problems with high Knudsen numbers.
The researchers developed a new experimental technique for measuring the Knudsen number in micro-channels.
The researchers developed a new method for calculating the Knudsen number in complex geometries.
The researchers developed a new numerical method that is accurate for a wide range of Knudsen numbers.
The researchers developed a new theoretical framework for understanding the behavior of gases at high Knudsen numbers.
The researchers explored the impact of the Knudsen number on the performance of micro-pumps.
The researchers explored the impact of the Knudsen number on the performance of micro-reactors.
The researchers explored the impact of the Knudsen number on the performance of micro-scale fuel cells.
The researchers explored the influence of the Knudsen number on the performance of micro-nozzles.
The researchers explored the influence of the Knudsen number on the performance of micro-scale compressors.
The researchers investigated the influence of the Knudsen number on the heat transfer rate.
The researchers presented a detailed analysis of the flow field as a function of the Knudsen number.
The results showed a clear dependence of the slip length on the Knudsen number.
The simulation results showed a strong correlation between the Knudsen number and the flow field.
The simulation results were compared to analytical solutions valid for low Knudsen numbers.
The simulation was carefully designed to maintain a consistent Knudsen number throughout the domain.
The slip velocity at the wall becomes more pronounced with an increasing Knudsen number.
The study focused on investigating the flow characteristics at intermediate Knudsen numbers.
The theoretical model accurately predicts the flow behavior for small Knudsen numbers.
The transition from slip flow to free molecular flow is governed by the Knudsen number.
The transition regime is characterized by Knudsen numbers between 0.01 and 10.
The use of kinetic theory is necessary when the Knudsen number is no longer negligible.
The validity of the slip-flow assumption hinges on keeping the Knudsen number relatively small.
Understanding the behavior of gases at high Knudsen number is crucial for space exploration.
We need to reduce the pressure significantly to achieve a sufficiently high Knudsen number for our experiment.
We used the Knudsen number to classify the flow regime in our microchannel.