Interaction of Sedimenting Drops in a Miscible Solution – Formation of Heterogeneous Toroidal-Spiral Particles

Toroidal-spiral structures form through the interaction of horizontally and vertically displaced drops sedimenting in a miscible bulk solution. These polymeric drops are then solidified into particles, which can be potentially used to encapsulate and deliver multiple active compounds on separate schedules. Sedimentation regimes and drug release were quantified.

affected by the glycerol concentration. Ethanol and DI water were added in both phases to adjust the density difference.

Reaction Scheme of PEG-DA Cross-linking
Initiator, I-2959, dissolved in ethanol was added to PEG-DA to enable sub-second crosslinking with a high intensity (~10 W/cm 2 ) ultra violet (UV) lighting system (Bluewave 75, Dymax, Torrington, CT). In the experiments, UV light in the wave-length range of 280-450nm was used to initiate radical formation from I-2959 (Fig. S1). These free radicals cross-link the polymer into a dense matrix by breaking double bonds on the acrylated end groups of PEG-DA. 2 Fig. S1. Free radical formation from I-2959 due to UV light exposure, which can be used to cross-link acrylated polymers. The horizontally displaced drops were generated by using an array of glass capillaries (ID: 536.2 µm, OD: 658.3 µm). The glass capillaries were embedded in an epoxy plug inside one end of a section of polyurethane tubing (ID: 2.4 mm, OD: 4.0 mm). The other end of the tubing was connected to a gastight glass syringe. The device was assembled by fixing the position of the glass capillaries under the stereoscope. To ensure that the glass capillaries were completely parallel, they were tacked onto two plastic bars with epoxy (Fig. S2). The flow rate was set to be 15 ml/min. The glass capillaries were buried below the surface of the bulk solution. For a given device, the distance between the glass capillaries was fixed. However, the dimensionless distance could be varied by changing the sizes of the drops. Target volumes ranged from 0.02mL to 0.13mL to produce dimensionless distances from 2 to 4.5 as presented in Fig. 5.

Fig. S2
Device consisting of three glass capillaries.
To illustrate that multiple compounds can be encapsulated into one TS particle, we placed four smaller drops surrounding a relatively bigger polymer drop. The injection device was constructed in a similar way as above, except with the capillaries in a five-spot pattern. The center capillary was fed by one syringe pump with target volume (0.03 mL), while the other four capillaries were fed by a pair of syringes driven by a second pump with target volume (0.003 mL). Therefore, the dispensed volume for each surrounding drop was 0.0015mL.

Acquisition of High-Speed Camera Images
All the time sequences of drops were obtained by using a high-speed camera (Prosilica GX 1050, Allied Vision Technology, Germany) with a magnification lens (MLH-10X, Computar, Commack, NY). The capture speed was set to a nominal speed of 67 frames per second. Exposure was set to 1 milli-second.

Definition of Dimensionless Groups
Reynolds number (Re) represents the ratio of inertial forces to viscous forces. It is calculated from the expression, Various suitable compositions of the trailing drop are listed in Table S2.  (1) where is the density difference between the th drop and the bulk liquid, is the gravitational acceleration vector, and is the Green's function for creeping flow (Stokeslet tensor field), 3 As time progresses, the flow field (1) moves and deforms the drop domains that in turn determine it, resulting in nonlinear dynamics. For numerical computations, each drop domain is replaced with a statistically uniform swarm of many Lagrangian particles of the appropriate mass. The integral (1) is then approximated, in what amounts to a Monte Carlo method, with a sum over all particles from all drops. 4 This leads to a coupled, nonlinear system of ODEs for the coordinates of the particles, which is solved numerically with a fourth-order Runge-Kutta method. 5 If we use a total of particles to represent the drops, a direct summation over all particles to calculate the velocity of each of these particles leads to order operations. A particle-mesh method 6 is combined with the fast Fourier transform 7 to reduce the operation count to order with only minor losses in accuracy. 8