Microfluidic rheology of the multiple-emulsion globule transiting in a contraction tube through a boundary element method

Highlights

• Transition of multiple emulsions with various inner structures in a contraction is studied.

• Multiple-emulsion globules have large deformations and inner droplets squeeze each other.

• Movements of inner droplets are severely affected by inner circulations similar to Taylor flow.

• Complication and squeeze of internal structures subject the globule to higher pressure drops.

Abstract

Through a lately developed boundary element method, this paper investigates the rheology of the multiple-emulsion globule with various internal structures in a contraction tube. As fine templates to prepare microcapsules for targeted drug delivery, multiple emulsions (ME) with complex structures have been generated through microfluidics. The deformation and breakup of multiple emulsions in a microchannel are critical to the transport and release of their inclusion. However, the numerical investigation of the rheology of multiple emulsions in a contraction tube is only limited to a simple case, i.e., core-shell double emulsions (CSDE), currently. In this paper, the boundary element method is employed to investigate the deformation and displacement of 2-dimensional globules of three types of multiple emulsions, i.e., concentric ME with multiple layers, double emulsions containing multiple inner droplets and ME with asymmetric internal structures, in a contraction tube. Comparing to those of CSDE, the complication of internal structures and the collision among inner droplets will subject the globule to flows with higher pressure drops when the volume flow rates are fixed.

Introduction

Multiple emulsions are nested liquid systems, which have highly ordered internal structures consisting of multiple layers and probably containing one or more smaller engulfed droplets (Wang J.T. et al., 2011). Such complex emulsions have drawn much attention recently due to their broad potential applications in encapsulated drug delivery, food industry and cosmetics (McClements, 2012). Due to their complex inner structures, it is hard to prepare such fantastic particles with uniform structures and sizes. Fortunately, the development of droplet-based microfluidics provides a great platform to generate multiple emulsions with highly ordered and uniform internal structures during the past decade. Abate et al. (2011) used a microfluidic device consisting of a series of flow-focus junctions to form multiple emulsions with controllable shell thicknesses or droplet with functional magnetic core. Kim and Weitz (2011) generated monodisperse multiple-emulsion droplets of high order by using stable biphasic flows in confining channels through a one-step emulsification approach. Lately, Wang W. et al. (2011) fabricated multicomponent multiple emulsions in which the number, ratio and size of inner droplets are precisely controlled through a hierarchical and scalable microfluidic device (see Fig. 1).

Monodisperse globules of multiple emulsions have promising applications in co-encapsulating incompatible actives or chemicals for synergistic delivery or for biochemical or chemical reactions (Sun et al., 2010, Chen et al., 2008). These multiple-emulsion globules provide a protective shell for active reagents. The shell can provide isolation between the reactants and the environment, which may avoid the cross contamination with the environment, or may prevent harmful reaction products from being released to the environment. However, if the release is needed, the globules can be triggered to burst and release their payloads under strong outer shears. Thus, the rheology of multiple emulsions is critical under such a demand.

Up to now, only a few experimental investigations on the rheology of double emulsions have been reported (Ulbrecht et al., 1982, Chen et al., 2011a, Li et al., 2011, Panizza et al., 2008). Ulbrecht et al. (1982) primitively compared the stability and deformation of double emulsions in shear flows to those of homogeneous drops through a series of experiments in the early 1980s. Chen et al. (2011b) developed a microfluidic approach for flow-controlled coalescence of different cores inside double emulsions to carry out reactions, which has potentials for the fabrication of high viscosity particles and for cell assays and screening. Under the flow shears and the geometry constraint of channels, the spherical particles of double emulsions were deformed and then further converted into rod-like microcapsules through photo-polymerization (Panizza et al., 2008). Recently, the controlled breakup of double emulsions as they flow through an orifice of a tapered nozzle was investigated, and a flow regime where the inner core of double emulsions can be released was identified (Chen et al., 2011a, Li et al., 2011).

Through the assembling of the co-axial flow modules of droplet generation and deformation, non-spherical particles can be engineered and produced (Panizza et al., 2008). Actually, the micro-device is just like a contraction tube in which the downstream narrow channel plays the role of the deformation module. In the drug delivery and oil recovery, the encapsulating structures must go through blood capillaries in the human body or the porous material of a reservoir which are both media with constrictions (Chen et al., 2011a, Li et al., 2011). Sometimes, the active ingredient in the multiple emulsions must be released in these constrictions. In contrast, some encapsulated particles should remain intact when they move through the constriction, and will breakup only when they reach the targeted release location. Lately, microfluidic devices like contraction geometries have also been one of important tools to investigate the interfacial rheology of complex fluid (Pipe and McKinley, 2009, Martin et al., 2011). Thus, the rheology behavior of multiple-emulsion particles in a contraction is very interesting and should be investigated carefully.

Various mathematical methods (Stone and Leal, 1990, Toose et al., 1999, Smith et al., 2004, Zhou et al., 2008, Song et al., 2010, Leong et al., 2011, Gao and Feng, 2011, Qu and Wang, 2012) have been employed to investigate the rheology of multiple emulsions numerically. Among these numerical works, Stone and Leal (1990) dealt with the deformation and breakup of concentric double emulsions in infinite extensional flows by applying the boundary integral method. Zhou et al. (2008) investigated the morphological evolution of a compound drop moving along the centreline of a circular contraction in a pressure-driven pipe flow. The entry of breast cancer epithelial cells into a micro-channel was studied through both simulation and experiment (Leong et al., 2011). Lately, Qu and Wang (2012) investigated the dynamics of concentric and eccentric globules of core-shell double emulsions suspended in extensional flows through a 3D spectral boundary element method, which is a good development since Stone and Leal's (1990) pioneer work . Nevertheless, all previous works are only limited to core-shell double emulsions (CSDE). Although Pal, 2007, Pal, 2011 investigated the viscosity equation of double emulsions containing multiple inner droplets (DEMID), he approximately modeled the DEMID as CSDE first in order to derive the equation. Thus, the systematic investigation on the rheology of multiple emulsions with complex internal structures is still lacking.

Recently, our group (Wang et al., 2013a, Wang et al., 2013b) developed a boundary integral method which can treat the rheology of multiple emulsions with orderly structures up to n layers and up to m_i droplets in the i-th layer in microchannels with various geometries. However, we only investigated the small deformation of multiple-emulsion globules suspended at the center of a cross-slot under a modest extensional flow in previous works (Wang et al., 2013a, Wang et al., 2013b). The effects of the confined geometries on the large deformation and displacement of multiple-emulsion globules have not been investigated.

In this paper, we will use the well developed method to study the deformation and displacement of multiple-emulsions globule in a contraction tube. The effects of the internal complex structures are particularly interested. In the next section, the numerical method is introduced briefly. In Section 3, the results of the rheology of multiple-emulsion globules with diverse internal structures in the confined geometry are presented, in which effects of internal structures on the pressure drop of the flow of the continuous phase and the hydrodynamics of the globules are particularly investigated.