Designing Colloidal Molecules with Microfluidics

The creation of new colloidal materials involves the design of functional building blocks. Here, a microfluidic method for designing building blocks one by one, at high throughput, with a broad range of shapes is introduced. The method exploits a coupling between hydrodynamic interactions and depletion forces that controls the configurational dynamics of droplet clusters traveling in microfluidic channels. Droplet clusters can be solidified in situ with UV. By varying the flow parameters, clusters are prescribed a given size, geometry, chemical and/or magnetic heterogeneities enabling local bonding. Compact structures (chains, triangles, diamonds, tetrahedrons,...) and noncompact structures, such as crosses and T, difficult to obtain with current techniques are produced. Size dispersions are small (2%) and throughputs are high (30 000 h−1). The work opens a new pathway, based on microfluidics, for designing colloidal building blocks with a potential to enable the creation of new materials.


Supplementary Material 1 : Droplet number per cluster
Bingqing Shen, Joshua Ricouvier, Florent Malloggi and Patrick Tabeling* When the plugs produced at the T-junction reach the step, they break up into droplets. The number of droplet per cluster that results from this process depends on the flow-rates of the two phases. Here 1). There exist plateaus on which the droplets are identical and, thereby, N is an integer. In between, the clusters include several droplets of different sizes the droplet number N is defined as the total cross-sectional area of the cluster divided by the area of the larger droplet. For a fixed flow-rate of the external phase, this number increases with the plug volume, in a stepwise manner (see Supplementary Figure -several identical, one smaller -, giving rise to snowman shapes, or heterogeneous chains. For such cases, N is a non integer number. In fact, this evolution has the form of a devil's staircase, reminiscent of the nonlinear interaction between two frequencies, one being associated to the plug generation at the T junction, and the other to the droplet formation at the step. [25] Figure S1: Devil's staircase of droplets production. Droplet number (defined as the total cross-sectional area of the cluster divided by the area of the larger droplet) as a function of plug volume, for a fixed flow-rate of the external phase (w=50µm, h 1 =10µm). (b) Plug volume as a function of Q disperse /Q continuous for microfluidic systems (W=50µm, h 1 =10µm).

Bingqing Shen, Joshua Ricouvier, Florent Malloggi and Patrick Tabeling*
The control flow influences the initial configuration of the cluster at the step, along with the distances between successive clusters in the SA channel. This is shown in the Figure below, for triplets. Here we maintain the pressures of the dispersed and continuous phases constant (resp. equal to 38 and 11 mbar), and we increase the pressure P C at the control entries. Figure S2: Spacing control between the clusters in SA channel. Different configurations observed at various P c , in a system where W=50µm, h 1 =10µm, h 2 =160µm. (a) PC= 20mbar. The distance between clusters is 100µm. (b) PC= 80mbar. The distance between clusters is 400µm. (c) PC= 120mbar. The distance between clusters is 1100 µm. The scale bar is 100µm. As the pressure at the control entries raises up, the orientation of the cluster at the entry tends to align with the mean flow, and, in the meantime, the distances between two successive trimers in the SA channel increase, as the result of mass conservation.  ). In this paper, the two dimensional dynamics of a system of N identical droplets, with speeds smaller than the upstream flow, was modelled. In our case, we must modify these equations, by adding two terms, one representing the adhesion forces between identical droplets (see for instance

Supplementary
Foundations of Colloidal Science, Snd Ed., R.Hunter, p 542), and the other corresponding to the short-range repulsive forces that prevents droplet interpenetration. With such modifications, the system reads: in which is the speed of droplet i (with ! " the center's position, R its radius), the unit vector projected onto the mean flow at infinity, β the reduction factor of the cluster speed (due to friction against the wall, as discussed in the paper), the separation distance between droplets i and j, A a constant, η the external phase viscosity, F ij a short range repulsive term that prevents droplet interpenetration.
To obtain the dimensionless equations (1), one introduces the following dimensionless quantities.

VIDEO LIST
Bingqing Shen, Joshua Ricouvier, Florent Malloggi and Patrick Tabeling* Movies S1 -3: Kinetics of clusters formation Fluorinated oil droplets are suspended in an aqueous solution containing surfactant (2% w/w SDS). Movies are acquired at 25 fr/s and played at a rate slowed down 2.5 times. Scale bar, 100 µm.

Movie S4: Kinetics of hybrid clusters formation
Alternating transparent and blue plugs are formed at the T-junctions, and transported at the step. The transparent plug breaks into two spherical droplets while the blue one forms a single droplet. In this way, a heterotrimer is formed. The video is acquired at 50 fr/s and played real time. Scale bar, 100 µm.

Movie S5: 3D tetrahedron self assembly
Fluids are fluorinated oil in water with 2% SDS and 5%NaCl. Here, d=(0µm. Video is recorded at 25 fr/s and played at a rate slowed down 2.5 times