Enrichment of Scavenged Particles in Jet Drops Determined by Bubble Size and Particle Position

When small bubbles rupture in a contaminated water source, the resulting liquid jet breaks up into droplets that can aerosolize solid particulates such as bacteria, viruses, and microplastics. Particles collected on the bubble surface have the potential to become highly concentrated in the jet drops, dramatically increasing their impact. It has been assumed that only particles small enough to fit within a thin microlayer surrounding the bubble can be transported into its influential top jet drop. Yet here, we demonstrate that not only can larger particles be transported into this jet drop, but also that these particles can exceed previous enrichment measurements. Through experiments and simulations, we identify the prerupture location of the liquid that develops into the top jet drop and model how interfacial rearrangement combines with the bubble size, particle size, and the angular distribution of particles on the bubble surface to set the particle enrichment.

Figure 1

Polystyrene microparticles (radius $r_p=7.5$ and $15\mathrm{\mu }\mathrm{m}$) exhibit enrichment peaks in jet drops. (a) Schematic of experiments: bubbles rise a height $H$ through a solution of uniform particle size at concentration $C\text{particles}/\mathrm{mL}$. The bubble scavenges particles as it rises and the top jet drop is collected. (b) A bubble with radius $R_b=350\mathrm{\mu }\mathrm{m}$ creates a jet drop with radius $r_d=43\mathrm{\mu }\mathrm{m}$ that contains $N_d=43$ particles, corresponding to an enrichment factor $\mathcal{E}=1300$. (c) Measured enrichment [Eq. (1)] for both particle sizes and historical data from Blanchard and Syzdek [22].

Figure 2

The modified filtration mechanism is developed numerically for a $R_b=350\mathrm{\mu }\mathrm{m}$ bubble. (a) Bubble rupture creates a fluid jet at time $t_c$ [(i)–(iii)], which then forms a jet drop $r_d$ [(iv)–(v)]. Lagrangian particle tracking reveals that not all of the fluid in the microlayer $\ell$ [(vi), left] ends up in the top drop [(vii), left]. Reverse Lagrangian tracking finds that the fluid in the top drop [(vii), right] comes from a layer whose thickness $h_0$ varies with angle $\theta$ at $t=0$ [(vi), right], where the thickness has been exaggerated for clarity. (b) Plot comparing $h_0$ to $\ell$ highlights a strong dependence on the initial angle $\theta$. (c) Schematic illustrating the proposed particle exclusion mechanism. The bubble interface on which particles are attached compresses from a surface area $d{A}_0$ to $d{A}_c$, which locally thickens $h_0$ to $h_c$ and provides an exclusion criterion when $r_p>h_c$. (d) Local compression $d{A}_0/d{A}_c$ normalized by $(R_b/r_d{)}^2$ approaches one. (e) The compressed thickness $h_c$ varies with angle and reaches nearly half the jet drop size. A particle with $r_p=0.45r_d$ (red dotted line) would be excluded from the top jet drop; whereas a smaller particle $r_p=0.15r_d$ (yellow dashed line) would be included only at certain angles on the bubble, following the proposed exclusion criteria.

Figure 3

Extending numerics to additional bubble sizes via an Ohnesorge number, Oh. (a) Experimental and numerical values of $r_d/R_b$ vary with $\mathrm{Oh}\equiv \mu /\sqrt{\rho \gamma R_b}$, where $\mu$, $\rho$, and $\gamma$ are the liquid viscosity, density, and surface tension, respectively. Values are consistent with existing theory (solid [19] and dashed lines [21]). (b) The thickness $h_0/\ell$ depends on both angle $\theta$ and Oh. (c) Plots of $h_c/r_d$ similarly show that for higher Oh the top jet drop fluid is drawn from an increasingly smaller portion of the bubble.

Figure 4

Particle transfer efficiencies $E_t$ between experiments and models are compared. (a) Experimental transfer efficiency is approximated as $E_t=(4R_b/3H)(\ell /r_p)\mathcal{E}$ for the present study as well as for Refs. [22] and [29]. Previous enrichment models have relied on the microlayer thickness $\ell$ and underpredict values of $E_t$ (solid [25] and dashed lines [29]). (b) The transfer efficiency modeled by Eq. (3) depends on both $r_p/r_d$ and Oh (solid lines). These values can be plotted with contours of constant Oh (main) or contours of constant $r_p/r_d$ (inset) from numerics. In all experiments, both $r_p/r_d$ and Oh change as the bubble size varies. The modeled $E_t$ values are consistent with our experimental results for which $0.004<\mathrm{Oh}<0.007$.