Baldas, Lucien

Barrot, Christine

Colin, Stéphane

López Quesada, Guillermo

Rojas-Cárdenas, Marcos

Tatsios, Giorgos

Valougeorgis, Dimitris

English

HAL-INSA Toulouse

Computational study of a novel Knudsen pump design exploiting drilling and 3D printing techniques in low thermal conductivity materials

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Computational study of a novel Knudsen pump design
exploiting drilling and 3D printing techniques in low
thermal conductivity materials
Guillermo López Quesada, Giorgos Tatsios, Stéphane Colin, Dimitris
Valougeorgis, Lucien Baldas, Christine Barrot, Marcos Rojas-Cárdenas
To cite this version:
Guillermo López Quesada, Giorgos Tatsios, Stéphane Colin, Dimitris Valougeorgis, Lucien Baldas,
et al.. Computational study of a novel Knudsen pump design exploiting drilling and 3D printing
techniques in low thermal conductivity materials. 6th Micro and Nano Flows Conference, Professor
Srinivas Garimella, Georgia Institute of Technology, Sep 2018, Atlanta, United States. pp.9 - 12.
￿hal-02105734￿
6th Micro and Nano Flows Conference 
Atlanta,USA, 9-12 September 2018 
 
Computational study of a novel Knudsen pump design exploiting drilling and 3D 
printing techniques in low thermal conductivity materials 
 
Guillermo LOPEZ QUESADA 1,2*, Giorgos TATSIOS 2, Stéphane COLIN 1, Dimitris VALOUGEORGIS 2,  
Lucien BALDAS 1, Christine BARROT 1, Marcos ROJAS-CARDENAS 1 
 
* Corresponding author: Tel.: 0034618512360; Email: lopezque@insa-toulouse.fr 
1. Institut Clément Ader (ICA), Université de Toulouse, CNRS, INSA, ISAE-SUPAERO, Mines Albi, UPS, Toulouse, France 
2. Dept. of Mechanical Engineering, University of Thessaly, Volos, Greece 
 
 
Keywords: Vacuum micropump, thermal transpiration, kinetic modeling. 
 
Over the past two decades a large number of MEMS and 
micro-devices have been developed. These miniaturized systems, 
such as lab-on-chip sensors, gas chromatography analyzers, etc., 
require micro-pumps for air sampling through the testing stages of 
the device. Additionally, some microscale components such as 
radio frequency switches, microscopic vacuum tubes and other 
parts that depend on electron or ion optics, require certain vacuum 
environment for proper operation. Simply sealing the devices is not 
sufficient because leaks and outgassing are excessively detrimental 
in vacuum devices at microscale level. Accordingly, such 
components may need vacuum pumping to maintain proper 
functionality. 
The thermal transpiration phenomenon has been extensively 
investigated; however, functional prototypes based on this 
phenomenon have been only recently developed. The Knudsen 
pump, which is one of the devices exploiting this well-known 
phenomenon, is able to generate a macroscopic gas flow by solely 
exploiting a tangential temperature gradient along a surface without 
requiring any external pressure gradient [1]. Still, fabricating a 
Knudsen pump is not a trivial task mainly due to microfabrication 
difficulties and constraints linked to the control of local thermal 
gradients [2, 3]. 
In this work, a novel Knudsen pump is proposed. Instead of 
following the typical process of etching along the substrate surface, 
the microchannels are fabricated by laser drilling or 3D printing 
techniques across the thickness of the wafer, as shown in Fig. 1. In 
this novel layout of the Knudsen pump, the microfabrication 
process is fundamentally simplified. Furthermore, the 
implementation of low thermal conductivity materials such as glass 
or polymers decreases the overall power consumption of the device 
and increases the thermal gradient that can be achieved along the 
wall of the channels. Additionally, by manufacturing the channels 
through the thickness of the device, the hot and cold regions of the 
Knudsen pump are spatially separated resulting to an easier 
temperature control. Using this design, three different 
configurations can be developed (Fig. 1): 
A. Multiple parallel channels for high mass flow rate and 
low pressure difference. 
B. Multistage assembly of single channels in series for high 
pressure difference and low mass flow rate. 
C. Combination of the two previous configurations to find a 
compromise between achieved pressure difference and 
mass flow rate. 
The two important performance metrics for these micropumps are 
the mass flow rate ṁ and the pressure difference ΔP between the 
inlet and the outlet of the pump. Depending on the target 
application of the Knudsen pump, the required performance can 
vary considerably. The idea is that for a particular surface area, 
depending on the application of the Knudsen pump, channels can 
be arranged all in parallel to maximize ṁ (configuration A), all in 
series to maximize ΔP (configuration B) or to compromise between 
the limiting conditions (configuration C). 
Figure 1. Representative view of the three different configurations; yellow arrows denote the pumping flow direction. 
6th Micro and Nano Flows Conference 
Atlanta,USA, 9-12 September 2018 
The numerical study is based on the linearized Shakhov kinetic 
model subject to diffuse boundary conditions. The deduced kinetic 
coefficients are introduced in a mass balance equation to yield the 
flow rate and the pressure difference [4]. The computational 
investigation involves the analysis of configurations A and B, so 
that their solutions are combined to characterize configuration C. 
Here, results for a representative configuration C are presented. 
Each pumping sub-stage is taken to be a square area of 200 μm x 
200 μm with 100 channels of diameter D = 10 μm in parallel 
(easily achieved by various microfabrication processes). Each 
backflow sub-stage is also a square area of 200 μm x 200 μm with 
a single channel of diameter D = 100 μm. The length of the 
channels is L = 300 μm (following the typical thickness of glass 
wafers). The temperatures at the cold and hot sides of the channels 
are TC = 300 K and TH = 400 K respectively (following previous 
experimental experience [5]). The numerical simulations have been 
performed for various operating inlet pressures Pin = 1 kPa, 5 kPa, 
10 kPa, 20 kPa, 50 kPa and 100 kPa and considering argon as the 
working gas. 
As it was expected from previous analysis in multistage systems 
with orthogonal channels [4], in most cases ΔP increases almost 
linearly with the number of stages (Fig 2-top). Only, in the case of 
the lowest operating pressure of 1 kPa, the pressure difference is 
not increased in an exactly linear manner in the first stages due to 
the non-linearity at higher rarefaction flow regimes (transitional 
regime). Depending on the size of the channel, the maximum ΔP is 
found at a gas rarefaction parameterr δ = 4-8, which for the channel 
diameter D = 10 μm corresponds to an operating inlet pressure 
around 5 kPa. This finding has been also experimentally observed 
[5]. This remark also justifies the fact that ΔP increases as the inlet 
pressure inP  decreases until reaching the maximum performance 
at Pin = 5 kPa and then, for Pin = 1 kPa is slightly decreased. This is 
more evident for a small number of stages, where δ is small, while 
as the number of stages increases and δ is also increased the 
difference in ΔP is decreased and finally, by the 100th stage both 
cases of Pin = 1 and 5 kPa provide about the same performance. 
Regarding the mass flow rate ṁ (Fig 2-bottom), it drops rather 
rapidly as the number of stages is increased from one up to ten 
stages and then, as the number of stages is further increased, it is 
reduced very slowly in an asymptotic manner. The reduction of the 
mass flow rate depends on the operating pressure, being bigger 
when the flow regime is more rarefied (at 1 kPa the reduction is 
25%) in opposition to the very low reduction closer to the 
hydrodynamic regime (at 100 kPa the reduction is only 1%). This 
evolution of ΔP and the mass flow rate with the number of stages is 
interesting for designing a multistage pump since by increasing the 
number of stages to more than ten the pressure difference grows 
linearly, while the mass flow rate remains almost constant. 
As a conclusion, a novel design for a Knudsen pump has been 
presented and computationally explored by taking into 
consideration tentative manufacturing and experimental constraints. 
The proposed design aims to achieve particular performances for 
targeted applications by tailoring the pumping stages (either 
increasing the parallel channels for enhancing the mass flow rate or 
increasing the number of stages to boost the pressure difference). It 
is noted that the presented results up to 100 stages only needs a 
footprint of 8 mm2, which is more than four thousand times smaller 
than previous designs [2, 3]. Therefore, the compactness of the 
design is very good. Finally, a prototype is being manufactured and 
corresponding experimental work is expected to begin shortly. 
 
Acknowledgements 
This project has received funding from the European Union’s 
Framework Programme for Research and Innovation Horizon 2020 
(2014-2020) under the Marie Skłodowska-Curie Grant Agreement 
No. 643095. 
 
References 
[1] Colin, S. (2013). Single-phase gas flow in microchannels. Heat 
transfer and fluid flow in minichannels and microchannels. 
Elsevier. 11-102. 
[2] Qin, Y., An, S., et al. (2015) Arrayed architectures for 
multi-stage Si-micromachined high-flow Knudsen pumps, 
Journal of Micromechanics and Microengineering, 25 (11), 
115026. 
[3] An, S., Gupta, N. K., et al. (2014) A Si-micromachined 162-stage 
two-part Knudsen pump for on-chip vacuum, Journal of 
Microelectromechanical Systems, 23 (2), 406-416. 
[4] Tatsios, G., Lopez Quesada, G., et al. (2017). Computational 
investigation and parametrization of the pumping effect in 
temperature driven flows through long tapered channels. 
Microfluidics and Nanofluidics, 21(5)99. 
[5] Rojas-Cárdenas, M. (2012). Temperature gradient induced 
rarefied gas flows. PhD Thesis. Aix-Marseille Université. 
Figure 2. Pressure difference (top) and mass flow rate (bottom) of a 
configuration C multistage pump in terms of number of stages at various 
operating pressures. 


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Computational study of a novel Knudsen pump design exploiting drilling and 3D printing techniques in low thermal conductivity materials

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