Modeling drug delivery from multiple emulsions

Evolution dynamics of thin liquid structures investigated using a phase-field model

Liquid structures of thin-films and torus droplets are omnipresent in daily lives. The morphological evolution of liquid structures suspending in another immiscible fluid and sitting on a solid substrate is investigated by using three-dimensional (3D) phase-field (PF) simulations. Here, we address the evolution dynamics by scrutinizing the interplay of surface energy, kinetic energy, and viscous dissipation, which is characterized by Reynolds number Re and Weber number We. We observe special droplet breakup phenomena by varying Re and We. In addition, we gain the essential physical insights into controlling the droplet formation resulting from the morphological evolution of the liquid structures by characterizing the top and side profiles under different circumstances. We find that the shape evolution of the liquid structures is intimately related to the initial shape, Re, We as well as the intrinsic wettability of the substrate. Furthermore, it is revealed that the evolution dynamics are determined by the competition between the coalescence phenomenology and the hydrodynamic instability of the liquid structures. For the coalescence phenomenology, the liquid structure merges onto itself, while the hydrodynamic instability leads to the breakup of the liquid structure. Last but not least, we investigate the influence of wall relaxation on the breakup outcome of torus droplets on substrates with different contact angles. We shed light on how the key parameters including the initial shape, Re, We, wettability, and wall relaxation influence the droplet dynamics and droplet formation. These findings are anticipated to contribute insights into droplet-based systems, potentially impacting areas like ink-jet printing, drug delivery systems, and microfluidic devices, where the interplay of surface energy, kinetic energy, and viscous dissipation plays a crucial role.

Release of molecules from nanocarriers

Release of drugs or vaccine molecules from macro-, micro-, and nano-sized carriers is usually considered to be limited by diffusion and/or carrier dissolution and/or erosion. The corresponding experimentally observed kinetics are customarily fitted by using the empirical Weibull and Korsemeyer-Peppas expressions. With decreasing size of carriers down to about 100 nm, the timescale of diffusion decreases, and accordingly the release can be kinetically limited, i.e., controlled by jumps of molecules located near the carrier-solution interface. In addition, nanocarriers (e.g., lipid nanoparticles) are often structurally heterogeneous so that the absorption of molecules there can be interpreted in terms of energetic heterogeneity, i.e., distribution of energies corresponding to binding sites and activation barriers for release. Herein, I present a general kinetic model aimed at such situations. For illustration, the deviation of the molecule binding energy from the maximum value was considered to be about 4-8 kcal mol-1. With this physically reasonable (for non-covalent interaction) scale of energetic heterogeneity, the predicted kinetics (i) are linear in the very beginning and then, with increasing time, become logarithmic and (ii) can be nearly perfectly fitted by employing the Weibull or Korsmeyer-Peppas expressions with the exponent in the range from 0.6 to 0.75. Such values of the exponent are often obtained in experiments and customarily associated with non-Fickian diffusion. My analysis shows that the energetic heterogeneity can be operative here as well.

Characterization of the Shells in Layer-By-Layer Nanofunctionalized Particles: A Computational Study

Drug delivery carriers are considered an encouraging approach for the localized treatment of disease with minimum effect on the surrounding tissue. Particularly, layer-by-layer releasing particles have gained increasing interest for their ability to develop multifunctional systems able to control the release of one or more therapeutical drugs and biomolecules. Although experimental methods can offer the opportunity to establish cause and effect relationships, the data collection can be excessively expensive or/and time-consuming. For a better understanding of the impact of different design conditions on the drug-kinetics and release profile, properly designed mathematical models can be greatly beneficial. In this work, we develop a continuum-scale mathematical model to evaluate the transport and release of a drug from a microparticle based on an inner core covered by a polymeric shell. The present mathematical model includes the dissolution and diffusion of the drug and accounts for a mechanism that takes into consideration the drug biomolecules entrapped into the polymeric shell. We test a sensitivity analysis to evaluate the influence of changing the model conditions on the total system behavior. To prove the effectiveness of this proposed model, we consider the specific application of antibacterial treatment and calibrate the model against the data of the release profile for an antibiotic drug, metronidazole. The results of the numerical simulation show that ∼85% of the drug is released in 230 h, and its release is characterized by two regimes where the drug dissolves, diffuses, and travels the external shell layer at a shorter time, while the drug is released from the shell to the surrounding medium at a longer time. Within the sensitivity analysis, the outer layer diffusivity is more significant than the value of diffusivity in the core, and the increase of the dissolution parameters causes an initial burst release of the drug. Finally, changing the shape of the particle to an ellipse produces an increased percentage of drugs released with an unchanged release time.

Modeling the diffusion-erosion crossover dynamics in drug release

A computational model is proposed to investigate drug delivery systems in which erosion and diffusion mechanisms are participating in the drug release process. Our approach allowed us to analytically estimate the crossover point between those mechanisms through the value of the parameter b (b_{c}=1) and the scaling behavior of parameter τ on the Weibull function, exp[-(t/τ)^{b}], used to adjust drug release data in pharmaceutical literature. Numerical investigations on the size dependence of the characteristic release time τ found it to satisfy either linear or quadratic scaling relations on either erosive or diffusive regimes. Along the crossover, the characteristic time scales with the average coefficient observed on the extreme regimes (i.e., τ∼L^{3/2}), and we show that this result can be derived analytically by assuming an Arrhenius relation for the diffusion coefficient inside the capsule. Based on these relations, a phenomenological expression for the characteristic release in terms of size L and erosion rate κ is proposed, which can be useful for predicting the crossover erosion rate κ_{c}. We applied this relation to the experimental literature data for the release of acetaminophen immersed in a wax matrix and found them to be consistent with our numerical results.

Stability and release mechanisms of double emulsions loaded with bioactive compounds; a critical review

Double emulsions (DEs), known as emulsions of emulsions, are dispersion systems in which the droplets of one dispersed liquid are further dispersed in another liquid, producing double-layered liquid droplets. These systems are widely used in the food and pharmaceutical industries due to their ability to co-encapsulate both hydrophilic and hydrophobic bioactive compounds. However, they are sensitive and unstable and their controlled release is challenging. In this study, first, the stability of DEs and their release mechanisms are reviewed. Then, the factors affecting their stability, and the release of bioactive compounds are studied. Finally, modeling of the release in DEs is discussed. This information can be useful to optimize the formulation of DEs in order to utilize them in different industries.

Dynamics of polydisperse multiple emulsions in microfluidic channels

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.

Phase-Field Modeling of Multiple Emulsions Via Spinodal Decomposition

Currently, multiple emulsions via liquid-liquid phase separation in ternary polymer solutions have sparked considerable interest because of its remarkable potential in physical, medical, and biological applications. The transient "onion-like" multilayers are highly dependent on the evolution kinetics, which is challenging to be scrutinized in experiments and has not yet been fully understood. Here, we report a thermodynamically consistent multicomponent Cahn-Hilliard model to investigate the kinetics of multiple emulsions by tracing the temporal evolution of the local compositions inside the emulsion droplets. We reveal that the mechanism governing the kinetics is attributed to the competition between surface energy minimization and phase separation. Based on this concept, a generalized morphology diagram for different emulsion patterns is achieved, showing a good accordance with previous experiments. Moreover, combining the analysis for the kinetics and the morphology diagram, we predict new emulsion structures that provide general guidelines to discovery, design, and manipulation of complex multiphase emulsions.

The vortex-driven dynamics of droplets within droplets

Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The observed dynamic regimes range from long-lived NES at low core-area fraction, characterised by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.