**6. Conclusions**

This work proposed a miniaturized, easily processed, and inexpensive XMFCD, which is based on 3D microfluidic channels and fabricated by LTCC. The single XMFCD (diameter 9 mm, thickness 1.4 mm) and dual XMFCD (diameter 9 mm, thickness 2.4 mm) samples were both produced, and their 3D microfluidic structures were both detected by X-ray which proves the feasibility of this method. Moreover, other XMFCDs with more layers can be fabricated based on LTCC in order to obtain bigger fluid resistance, which can meet smaller flow requirements of space electric thrusters. The flow characteristic mathematical model and the simulation diagram validated by experiment results can be used to analyze and design other gas flow control devices based on microfluidic channels. The influence analysis of the structural parameters on flow characteristics reveals that (1) the diameter of the orifice is the most important parameter, whose square is proportional to the mass flow; (2) the mass flow of N series orifices is approximately 1/ √ N of a single orifice's flow, which can be used to estimate the flow of XMFCDs with different layers; and (3) only when the groove's equivalent diameter is smaller than the orifice diameter, the impact of the groove on the XMFCD's flow will become significant. So this work proposed a novel processing method for realizing the miniaturization of XMFCDs which can also be used in other micro flow control fields, and the mathematic model and simulation method lays a theoretical foundation for research on the flow characteristic of micro gas flow control devices.

**Author Contributions:** Conceptualization, C.-B.G. and Y.S.; Data curation, K.N. and H.-H.H.; Formal analysis, M.-J.Z. and K.N.; Investigation, H.-H.H. and Z.-L.W.; Methodology, C.-B.G.; Project administration, Y.S. and Z.-P.Y.; Software, M.-J.Z. and Z.-L.W.; Writing—original draft, C.-B.G.; Writing—review & editing, M.-J.Z. and Z.-P.Y.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number 51805026.

**Conflicts of Interest:** The authors declare no conflict of interest.
