On analytical and experimental aspects of soap bubble stream charging

The paper discusses the applicability and advantages of using electrically charged soap bubbles as a route to produce fine sprays composed of highly charged particles, commonly named as electroaerosols. It is indicated that such low in energy demand process may produce very fine droplets or particulates charged to a level higher than that obtained using classical spray charging techniques, involving no bubbles. A process of a soap bubble electrical charging is thus initially studied on a simple analytical basis pointing out to a possibility of producing air bubbles with charge-to-mass (Q/m) ratio up to 60 mC/kg (constrained by the Rayleigh limit) while just 2 mC/kg is commonly considered as a threshold value for an effective particle charging process. Finite element 3D electrostatic simulation method (3D FEM) is then applied to assess a single bubble charging level achievable in a laboratory setup using a DC high-voltage biased bubble machine producing soap bubbles 23 mm in diameter on average. The 3D FEM simulation results postulate a single bubble maximum charging level approaching 25 nC at 41.5 kV charging voltage (constrained by the Rayleigh limit), corresponding to (Q/m) = 17.6 mC/kg. Finally, a stream of bubbles characterized by (Q/m) = 10.4 mC/kg was produced experimentally in the laboratory setup using a contact charging method at 40 kV DC supply. A discrepancy between 3D FEM-simulated results and experimental data was discussed on a shielding effect basis. Graphic abstract

Super-resolution of near-colliding point sources

We consider the problem of stable recovery of sparse signals of the form $$\begin{equation*}F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, \end{equation*}$$from their spectral measurements, known in a bandwidth $\varOmega $ with absolute error not exceeding $\epsilon>0$. We consider the case when at most $p\leqslant d$ nodes $\{x_j\}$ of $F$ form a cluster whose extent is smaller than the Rayleigh limit ${1\over \varOmega }$, while the rest of the nodes is well separated. Provided that $\epsilon \lessapprox \operatorname{SRF}^{-2p+1}$, where $\operatorname{SRF}=(\varOmega \varDelta )^{-1}$ and $\varDelta $ is the minimal separation between the nodes, we show that the minimax error rate for reconstruction of the cluster nodes is of order ${1\over \varOmega }\operatorname{SRF}^{2p-1}\epsilon $, while for recovering the corresponding amplitudes $\{a_j\}$ the rate is of the order $\operatorname{SRF}^{2p-1}\epsilon $. Moreover, the corresponding minimax rates for the recovery of the non-clustered nodes and amplitudes are ${\epsilon \over \varOmega }$ and $\epsilon $, respectively. These results suggest that stable super-resolution is possible in much more general situations than previously thought. Our numerical experiments show that the well-known matrix pencil method achieves the above accuracy bounds.

Numerical Investigation of Electrospray Working Performance on Ethanol

Electrospray as an alternative method to fabricate thin film is studied. High voltage is required by the electrospray system. The requirement of high voltage is different for various liquid depending on the surface tension property. Ethanol was used to resemble the solvent used in thin film deposition. From the experimental work, jetting performance did not occur despite of the high applied voltage which is around 1 KV. In this work, numerical calculation is carried out to find the reason behind of unsuccessful jetting at 1 KV applied voltage. The percentage of Rayleigh limit is around 0.4. Electrospray performance at walking distance 5 mm using ethanol is predicted to be stable when the applied high voltage is approximately 1.1 KV. The numerical investigation indicates that the jetting performance will occur if the applied voltage is more than 1.1 KV.