Osmotic release of drugs via deswelling dynamics of microgels: modeling of collaborative flow and diffusions.

Hydrogel colloids, i.e., micro- or nano-gels, are increasingly engineered as promising vehicles for polymer-based drug delivery systems. We report a continuum theory of deswelling dynamics of nanocomposite microgels driven by external osmotic shocks and further develop a universal framework, by introducing a buffer release domain, to quantitatively characterize a continuous drug release from deswollen microgels towards surroundings. The drug release is shown to proceed accompanied by an active outward solvent flow created by the elastically shrunken gel network. We further find that a declining trend in the cumulative release plateau with the drug size is followed by an apparent increase again as the drug size increases above a threshold. These findings highlight a nontrivial behavior that the resulting hydrodynamic interactions coexist collaboratively with the passive diffusions to facilitate a desired drug release. We show that deswelling of a stiffer microgel (the mesh size reduces slowly) or loading the larger drugs could bring a control-like release type, otherwise a burst-like release type emerges. Compared with a uniform microgel, the fuzzy-corona-like microgel enables a more productive drug release before reaching deswelling equilibrium. Our model not only predicts well the existing experiments, but also serves as a versatile paradigm to help understand the reciprocal roles of the solvent flow, the gel dynamics, and the diffusions in the polymer-based drug delivery systems.

Dynamic behaviors of sedimenting colloidal gel materials: hydrodynamic interactions.

It is a highly nonlinear poromechanics phenomenon that colloidal gel materials that are exposed to a gravitational stress greater than their yield stress undergo elastic compression. Here, we resolve theoretically the dynamic behaviors of colloidal gel settling in a closed cylindrical tube of finite height. We develop an extended phenomenological model by considering the hydrodynamic interactions between the backflow of the interstitial fluid and the sedimenting gel columns. We address the hydrodynamic signature by assembling a cylindrical streamer channel into pure Darcy's flow regime, and therefore our continuous model enables us to explore how geometric confinement exerted by the wall affects the colloidal gel sedimentation in a closed tube, which extends beyond the conventional poroelastic model. The results suggest a dynamically propagating strain rate from the gel bottom towards the settling gel front, which demonstrates the duality characteristics of fluidity and solidity for all gel types in our calculations. Our results confirm the vital role that geometric confinement has in association with hydrodynamic interactions in speeding up the sedimentation in gels because the average velocity of the settling front and the bulk sedimentation velocity of the gel particle (cluster) increase significantly under confinement. Furthermore, an analytical model we derive identifies the functional correlation of the velocity ratio to concentration in the compressive sedimentation regime of the gel. The numerical and analytical results collaboratively elucidate a signature that the compressive regime in the settling gel can be suppressed by the confinement, but strengthened again as the confinement increases to exceed a threshold. This threshold is shown to highly depend on the gel softness and initial particle loadings. Our systematic investigations benefit desirable strategies to manage the sedimentation dynamics of colloidal gel materials for application in various fields.

Gel dynamics in the mixture of low and high viscosity solvents: Re-entrant volume change induced by dynamical asymmetry.

When a gel swollen with a certain solvent is placed in the bath of another solvent, the gel swells or de-swells depending on the thermodynamic affinity to the gel. Toyotama et al. [Langmuir 22, 1952 (2006)] reported an unusual volume change of chemical gels that cannot be explained by the affinity difference: when a chemical gel saturated with water is immersed in ethylene glycol (EG), although those solvents have almost the same affinity to the polymer, the gel first shrinks and then re-swells and finally takes the same equilibrium volume as the initial. The re-entrant swelling was attributed to different diffusion rates between water and EG (dynamical asymmetry), but the detailed mechanism was not clarified. In this paper, we experimentally show that the characteristic times for the temporal shrinking and subsequent volume relaxation are proportional to the squared system size. This indicates that the phenomenon is governed by diffusive dynamics. According to this observation, we propose a coupled diffusion model explaining the physical mechanism of the re-entrant volume change.

Stratification in the dynamics of sedimenting colloidal platelet-sphere mixtures.

The dynamics of sedimentation in a binary mixture of colloidal platelets-spheres is studied theoretically using the minimal energy model. Revisiting a sedimenting mixture of platelets, we find that nematic phase behaviors are formed, coupled with certain stratification structures in the mixed sediments, which has never been discussed before. Non-equilibrium sedimentation-diffusion equations involving excluded volume interactions between the colloids have been developed to show the occurrence of the stratified structures in the mixed platelet-sphere sediments. The model shows clearly how the nematic configuration occurs corresponding to the stratifications (the peak-like concentration profiles) over time. Both initial sphere concentration and size ratio are found to have great effects on these two coupled structural configurations, which has been illustrated in two state diagrams in detail. It is found that the stratification structure of sphere-on-top corresponds to the nematic bottom phase configuration for a small size ratio; meanwhile, the platelet-on-top structure occurs corresponding to the floating nematic phase configuration for a large size ratio. Interestingly, we can specify a moderate range of size ratio in which the mixture displays only the nematic phase configuration (either the nematic bottom phase or the floating nematic phase depending on the sphere loadings), while the mixed sediments are unstratified as a bulk.

Dynamics of liquid crystalline phase transition in sedimenting platelet-like particles.

When a suspension of platelet-like particles sediment in a closed container, the particles undergo isotropic-nematic phase transition (I-N transition), and there appears a clear interface between the isotropic phase and the nematic phase. Usually the interface moves from bottom to top since the nematic phase appears and grows at the bottom, but it has been observed that in some situations the interface moves from top to bottom. Here, we study the dynamics of the interface by solving the non-equilibrium diffusion equation for the concentration of platelet-like particles, and show that the I-N interface can move upward (rising interface) or downward (falling interface) depending on whether the initial concentration is less than the critical concentration of I-N transition or more than it. We give a simple analysis theory for the motion of the interface in each case, which agrees well with the numerical calculations. We also show that the numerical results are in reasonable agreement with existing experimental measurements.

Dynamics of the floating nematic phase formation in platelet suspension with thickness polydispersity by sedimentation.

An inverted phase coexistence, where an ordered phase appears on top of a disordered phase, has been observed in polydisperse colloidal suspensions. Herein, we studied the dynamics of this phenomenon in a suspension of a mixture of two types of platelets, namely, thick and thin. We show that the thick platelets preferentially sediment first excluding the thin platelets, and create a region enriched with thin platelets at some place above the bottom, which eventually gives the inverted configuration. We show that such interplay between the sedimentation and the isotropic-nematic phase transition can cause a rich and complex sedimentation dynamic. Depending on the initial concentration and the gravity strength, the interface between the isotropic phase and the nematic phase can move up or down during the sedimentation, and a variety of final equilibrium structures can appear.

Self-growing nano-liquid-crystal film from dynamic swollen hydrogel substrates.

A hydrogel which spontaneously swells in an aqueous polymer solution was observed to produce a new hydrogel film coated on its swollen surface. Here, inspired by this phenomenon, we theoretically formulate the dynamics of isotropic-to-nematic (I-N) phase transition caused by swelling a hydrogel substrate (HS) in a dilute nanoplatelet suspension, and quantitatively characterize a self-growing nano-liquid-crystal (NLC) film coated on the swollen HS surface. We show that as the HS gets softer, the resulting NLC film can form earlier and achieve greater thickness (up to hundreds of micrometers). Our results and the existing experiments confirm that the growth dynamics of the NLC film or hydrogel film is exclusively regulated by the swelling behaviors of the HS instead of suspension configurations, e.g., I-N phase transition or sol-gel transition, suggesting a universal signature for the solutes ranging from molecules to colloids. However, both the maximum thickness of the NLC film and the corresponding characteristic time rely highly on the inherent elasticity of the HS and nanoplatelet aspect ratio. We demonstrate that the swelling quasiequilibrium state rather than the equilibrium state of the HS is more qualified to formulate a condition which is practically significant in preestimating the moment when the maximum thickness of the NLC film appears. Our theoretical framework serves as a robust paradigm to extensively rationalize (bio)film coatings which self-integrate with diverse nanostructural configurations via swelling-induced phase transition.

Transport dynamics of charged colloidal particles during directional drying of suspensions in a confined microchannel.

Directional drying of colloidal suspensions, experimentally observed to exhibit mechanical instabilities, is a nonequilibrium procedure that is susceptible to geometric confinement and the properties of colloidal particles. Here, we develop an advection-diffusion model to characterize the transport dynamics for unidirectional drying of a suspension consisting of charged particles in a confined Hele-Shaw cell. We consider the electrostatic interactions by means of the Poisson-Boltzmann cell approach with the viscous flow confined to the cell. By solving the nonequilibrium transport equations, we clarify how the multiple parameters, such as drying rate, confinement ratio, and the monovalent slat concentration, affect the transport dynamics of charged colloidal particles. We find that the drying front recedes into the cell with linear behavior, while the liquid-solid transition front recedes with power law behaviors. The faster evaporation rate creates a rapid formation of the drying front and produces a thinner transition layer. We show that confinement is equivalent to raising the effective concentration in the cell, and, accordingly, the drying front appears earlier and grows more rapidly. Under geometric confinement, a longer fully dried film is created while the total drying time is shortened. Moreover, we have theoretically illustrated that low salt loadings cause a large collective diffusivity of charged colloidal particles, which results in a colloidal network by aggregation. Thus, the drying behavior alters dramatically as salt loadings decrease, since the resulting compacted clusters of charged particles eventually convert the suspension into a gel-like material instead of a simple fluid. Our model is consistent with the current experiments and provides a simple insight for applications in directional solidification and microfluidics.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

A Novel Equivalent Agglomeration Model for Heat Conduction Enhancement in Nanofluids.

We propose a multilevel equivalent agglomeration (MEA) model in which all particles in an irregular cluster are treated as a new particle with equivalent volume, the liquid molecules wrapping the cluster and in the gaps are considered to assemble on the surface of new particle as mixing nanolayer (MNL), the thermal conductivity in MNL is assumed to satisfy exponential distribution. Theoretical predictions for thermal conductivity enhancement are highly in agreement with the classical experimental data. Also, we first try to employ TEM information quantitatively to offer probable reference agglomeration ratio (not necessary a very precise value) to just test rational estimations range by present model. The comparison results indicate the satisfactory priori agglomeration ratio estimations range from renovated model.

Fractal aggregation kinetics contributions to thermal conductivity of nano-suspensions in unsteady thermal convection.

Nano-suspensions (NS) exhibit unusual thermophysical behaviors once interparticle aggregations and the shear flows are imposed, which occur ubiquitously in applications but remain poorly understood, because existing theories have not paid these attentions but focused mainly on stationary NS. Here we report the critical role of time-dependent fractal aggregation in the unsteady thermal convection of NS systematically. Interestingly, a time ratio λ = tp/tm (tp is the aggregate characteristic time, tm the mean convection time) is introduced to characterize the slow and fast aggregations, which affect distinctly the thermal convection process over time. The increase of fractal dimension reduces both momentum and thermal boundary layers, meanwhile extends the time duration for the full development of thermal convection. We find a nonlinear growth relation of the momentum layer, but a linear one of the thermal layer, with the increase of primary volume fraction of nanoparticles for different fractal dimensions. We present two global fractal scaling formulas to describe these two distinct relations properly, respectively. Our theories and methods in this study provide new evidence for understanding shear-flow and anomalous heat transfer of NS associated non-equilibrium aggregation processes by fractal laws, moreover, applications in modern micro-flow technology in nanodevices.