# MEMS Vaporizing Liquid Microthruster: A Comprehensive Review
## 3 VLM Flow Instabilities  
The behavior of the flow inside a VLM is intrinsically unstable. The pressure, temperature, and mass flow rate oscillations typically occur in the inlet and the heating chambers, caused by the establishment of flow boiling instabilities, which dramatically affecting the micronozzle's expansion process by damaging the microthruster performance. It is worth underlining that the thrust instability created by boiling instabilities is also harmful for high-precision attitude control of micro-satellites. This intrinsic behavior was experimentally retrieved in all VLM designs, as confirmed in Figure 6, where the presence of two-phase flow instabilities was revealed by the thrust and pressure signals oscillating at a similar frequency and phase angle. In particular, the feeding pressure fluctuations strongly couples with the thrust force, which oscillates at a similar frequency and phase. The higher the heating temperature and the mass flow rate are, the greater the amplitude of the oscillations becomes. On the other hand, the oscillating frequency increases as a function of the boiling number \(Bo=q^{\prime}/(G\cdot h_{L})\), where \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref.** & \begin{tabular}{c} **\(T\)** \\ **(mN)** \\ \end{tabular} & \begin{tabular}{c} **\(I_{sp,max}\)** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **\(P_{d}\)** \\ **(W)** \\ \end{tabular} & \
\begin{tabular}{c} **\(\tau\)** \\ **(mN/W)** \\ \end{tabular} &
\begin{tabular}{c} **\(\eta_{O}=g_{O}I_{sp}\frac{T}{T_{a}}\cdot 100\)** \\ **(\%)** \\ \end{tabular} \\ \hline [PERSON] et al. [12] & 0.460 & 5.3 & 10.8 & 0.043 & 0.2 \\ [PERSON] et al. [13] & 0.120 & 17.5 & 2 & 0.060 & 10.3 \\ [PERSON] et al. [14] & 1.0–0.4 & 50–105 & 3.6 & 0.281–0.111 & 13.8–11.5 \\ [PERSON] et al. [15] & 0.003 & 7.8 & 0.81 & 0.004 & 0.03 \\ [PERSON] and [PERSON] [17] & 5.1 & 105 & N/A & N/A & N/A \\ [PERSON] et al. [20] & 0.068 & 6.9 & 9.2 & 0.007 & 0.05 \\ Cheah and Low [21] & 0.634 & 31 & 4.01 & 0.158 & 4.8 \\ [PERSON] et al. [22] & 0.970 & 18.7 & 9.31 \({}^{*}\) & 0.104 & 17.8 \\ [PERSON] et al. [24] & 1.54 & 51.1 & 7.87 & 0.196 & 9.8 \\ \hline \hline \end{tabular}  
* apparent voltage in VA.  
\end{table} 
Table 2: Comparison between the measured performance of existing VLMs. \(g_{0}=9.81\) m/s\({}^{2}\) is the gravitational acceleration at sea level. Figure 5: Manufactured VLMs in single channel configuration: (**a**) [PERSON] et al. [20]; (**b**) Cheah and Low [21]; (**c**) [PERSON] et al. [23]; (**d**) [PERSON] et al. [24]. \(q^{\prime}\) and \(G\) are the heat (in W/m\({}^{2}\)) and mass fluxes (in kg/m\({}^{2}\)/s), and \(h_{L}\) is the latent heat of vaporization in J/kg. Thus, a high boiling number causes significant impulse frequencies. Few literature reviews exist on boiling flow characterization into VLMs. In [16] and [17] a qualitative analysis of the most characteristic flow patterns into both single-channel, and a parallel microchannels configuration is reported. In a single-channel VLM, four boiling flow regimes were observed, namely:  
* Snake flow. When crossing into the heating channel, the liquid water stream flows with a snake motion. At the micronozzle exit, the main fluid stream is sprayed out of the microthruster from a limited area. * Vapor-droplet flow. Large liquid droplets, flowing along the heating channel, form. These droplets are splashed out of the micro-thruster from the entire nozzle exit. * Vapor-droplet-jet flow. A vapor jet, with dispersed tiny droplets, forms as a narrow stream with concentrated vapors and tiny liquid droplets ejected from the central area of the nozzle exit. * Vapor flow. Only vapor is evenly discharged from the nozzle exit of the microthruster. A pre-heating treatment of the empty micro-thruster at 573 K for 2 h revealed a vital step for appropriate operations of the microthruster. In this regard, the surface property changing from hydrophilicity to hydrophobicity after the heating treatment is presumed to cause snake flow disappearance.