Modeling pattern formation in soft flowing crystals

We present a mesoscale representation of near-contact interactions between colliding droplets which permits one to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focusing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet and bubble-based mesoscale porous materials.

Figure 1

Near-contact forces representation. Mesoscale modeling of near-contact interactions between two immiscible fluid droplets. ${\vec{F}}_{\text{rep}}$ represents the repulsive force and $\vec{n}$ is the unit vector perpendicular to the fluid interface. The vectors $\vec{x}$ and $\vec{y}$ indicate the positions, placed a distance $h$, taken within the fluid interface, and the dotted line tracks its outermost frontier. $A_{hM}$ and $A_{hm}$ are, respectively, the maximum and minimum value of the repulsive parameter.

Figure 2

(a) Collision sequence with $b=0.33$ and $\text{We}=10$. The upper row shows the experiments of Ref. [42] and the lower row shows the simulation results. (b) Left: Sequence of the flow field during the impact between the two droplets (midplane slice). During the first stage of the collision the dispersed phase flows outward, allowing the two droplets to approach. Afterward, when the droplets come in close contact, the fluid within the thin film begins to recirculate, thereby preventing film rupture, hence the coalescence between the droplets. (b) Right: Map of the local pressure deviation $\mathrm{\Delta }p/p_0=(p_0-p)/p_0$, where $p_0$ is the bulk pressure of the surrounding fluid and $p$ is the local pressure. As shown in the figure, the outer fluid is driven inward and consequently stabilizes the film.

Figure 3

(a), (b) Emulsion structures in microchannels. The different patterns are obtained by tuning the dispersed-to-continuous inlet flow ratios from $\varphi =u_d/2u_c=1–3.6$. Simulations are compared against the experiments of Raven and Marmottant [23]. (a) Hex-three, (b) Wet Hex-two, (c) Dry Hex-two, (d) Hex-one.

Figure 4

(a),(b) Spontaneous dynamic rearrangement of the emulsion pattern within the outlet microchannel [(a) numerical simulations, (b) experiments]. The vertical bars indicate the rearrangement fronts. Lower panel, experimental snapshot taken from [23].

Figure 5

Nonimensional pressure variation ($p_0$ is a reference bulk pressure) within the inlet main channel of the dispersed phase as a function of time. The dotted lines are linear fits to the data. The transition from a Hex-two to a Hex-one crystal is clearly indicated by a sudden jump in the slopes of the linear fits.