Numerical and experimental study of agglomerate dispersion in polymer extrusion

A model for agglomerate dispersion in screw extruders was developed and superimposed on the flow patterns as simulated using the FIDAP software. A particle tracking algorithm with an adaptive time step was used to follow the agglomerates trajectory. Along this flow path, the breakup probability was estimated using a Monte Carlo method and in conjunction with the local fragmentation number. Particle size distributions and Shannon entropy were computed along the screw channel. The results show good qualitative agreement between model predictions and experimental data

Conductive polymer foams with carbon nanofillers – Modeling percolation behavior

A new numerical model considering nanofiller random distribution in a porous polymeric matrix was developed to predict electrical percolation behavior in systems incorporating 1D-carbon nanotubes (CNTs) and/or 2D-graphene nanoplatelets (GNPs). The numerical model applies to porous systems with closed-cell morphology. The percolation threshold was found to decrease with increasing porosity due to filler repositioning as a result of foaming. CNTs were more efficient in forming a percolative network than GNPs. High-aspect ratio (AR) and randomly oriented fillers were more prone to form a network. Reduced percolation values were determined for misaligned fillers as they connect better in a network compared to aligned ones. Hybrid CNT-GNP fillers show synergistic effects in forming electrically conductive networks by comparison with single fillers

Compatibilization of titanium dioxide powders with non-polar media: Adsorption of anionic surfactants and its influence on dispersion stability

The effect of the adsorption of an anionic surfactant (aerosol OT, sodium dodecyl sulfate, sodium dodecyl sulfonate, or sodium dodecyl benzene sulfonate) on the dispersion behavior of some types of titanium dioxide pigments has been studied. Surfactant adsorption isotherms and the kinetics of the adsorption process were linked using a full Langmuir model. Sedimentation experiments were used to assess the dispersibility of the powders in two non-polar dispersion media (nonane and cyclohexane). Surfactant-modified powders were found to be more dispersible than the untreated powders in these non-polar media. Experiments were also performed to assess the stability of the surfactant coating to elevated temperatures and exposure to organic solvents

Mixing of immiscible liquids

Modeling of the basic processes that cover mixing of immiscible liquids starts with large dispersed drops; thus, at capillary numbers much larger than Cacril which is the critical ratio between the shear stress and the interfacial stress, above which no stable equilibrium dispersed drop shape exists. In that case, the interfacial stress is overruled by the shear stress (passive interfaces) and the (simple) principles of distributive mixing emerge, where deformation rate and time are interchangeable. Stretching and folding in a periodic flow should be realized for efficient mixing, and the occurrence of regular islands is to be avoided. The mathematical tools are available to numerically model distributive mixing even in three-dimensional transient flows, although the necessary computing time could be a constraint. Therefore the Mapping Method was developed that comprises a number of steps. First the boundaries of a large number of cells, forming a fine grid within the fluid, are accurately tracked during a short flow time. Subsequently, the deformed grid is superposed on the original undeformed one and their mutual intersections are computed reflecting, with normalized values between zero and one, the fraction of fluid that is advected from each cell to every other cell during flow time. Only the non-zero numbers (zero means that no fluid was exchanged between the cells in this flow time) are stored in a matrix that becomes huge if ...t is chosen large, the grid is fine and the problem is 3D. Using this matrix it is straightforward to compute, e.g., the concentration distribution after time M, since it follows from the mapping matrix - concentration vector (at t = 0) multiplication, which is a fast operation. The procedure is repeated during the total flow time t = N. M goingfrom step j . M to step (j + 1) . M with j = 1 ... N - 1. First the local concentration distribution on time j .M is averaged over each cell, which leads to some numerical diffusion. Next this concentration is mapped to step (j + 1) . M etc, up to N times. The method is elegant and fast, and allows for hundreds of thousands of computations in a reasonable time on a single processor PC, indeed making optimization ofdistributive mixing possible, investigating the influence of different geometries, protocols and processing parameters. As the local length scale decreases during the mixing process, the interfacial stress becomes ofthe same order as the shear stress (Ca == Cacrit ) and the long slender bodies formed disintegrate into lines of small droplets (dispersive mixing). Interfaces are active, and both deformation rate and time are important. Therefore, in transient flows the time scales of the competitive processes of deformation of the filaments, retraction, end-pinching, and growth of interfacial disturbances determine the size of the resulting dispersed fragments. Numerical models have been derived for these problems. Coalescence causes a coarsening of the morphology and the rate determining step is the drainage of the matrix fluid out of the gap between two adjacent drops. Interface mobility greatly influences the drainage rate, changing the process from pressure flow to dragflow. Surfactants are added, mainly to immobilize the interfaces, slowing down coalescence. Surfactants play an important role in break-up and coalescence, but the influence on the latter is most relevant. BIM, boundary integral methods, have been developed to study the local processes in detail. The final morphology, characterized by the average drop size, can be considered to be a result of a dynamic equilibrium between breakup and coalescence. For high volume fractions of the dispersed phase or low values of the viscosity ratio between dispersed phase and matrix, phase inversion can occur. DIM, diffuse interface methods, originally proposed by Cahn and Hilliard, allow computing these complex systems having topological changes in time and space in an elegant, easy to incorporate way. An issue remains regarding accurately resolving the thin interfaces on large domains

Applications of Statistical Physics to Mixing in Microchannels: Entropy and Multifractals

We apply rigorous measures of mixing based on entropy in conjunction with fractals to the field of microfluidics. First we determine the entropy and multifractal dimensions of images of mixing a fluorescent and a non-fluorescent fluid in a microchannel. We find the microstructures to be self-similar (fractals). Second we propose a new approach for patterning the walls of microchannels using the Weierstrass function. We have evidence from numerical simulations that by properly adjusting the dimension of the Weierstrass function one can get microfluidic devices that exhibit better mixing than the current ones. © 2008 Springer Netherlands