Mixing and Phase Separation of Fluid Mixtures

During the three years of the PhD project we extended the di®use interface (DI) method and apply it to engineering related problems, particularly re- lated to mixing and demixing of two °uids. To do that, ¯rst the DI model itself was validated, showing that, in agreement with its predictions, a single drop immersed in a continuum phase moves whenever its composition and that of the continuum phase are not at mutual equilibrium [D. Molin, R. Mauri, and V. Tricoli, "Experimental Evidence of the Motion of a Single Out-of-Equilibrium Drop," Langmuir 23, 7459-7461 (2007)]. Then, we de- veloped a computer code and validated it, comparing its results on phase separation and mixing with those obtained previously. At this point, the DI model was extended to include heat transport e®ects in regular mixtures In fact, in the DI approach, convection and di®usion are coupled via a nonequi- librium, reversible body force that is associated with the Kortweg stresses. This, in turn, induces a material °ux, which enhances both heat and mass transfer. Accordingly, the equation of energy conservation was developed in detail, showing that the in°uence of temperature is two-folded: on one hand, it determine phase transition directly, as the system is brought from the single-phase to the two-phase region of its phase diagram. On the other hand, temperature can also change surface tension, that is the excess free en- ergy stored within the interface at equilibrium. These e®ects were described using the temperature dependence of the Margules parameter. In addition, the heat of mixing was also taken into account, being equal to the excess free energy. [D. Molin and R. Mauri, "Di®use Interface Model of Multiphase Fluids," Int. J. Heat Mass Tranf., submitted]. The new model was applied to study the phase separation of a binary mixture due to the temperature quench of its two con¯ning walls. The results of our simulations showed that, as heat is drawn from the bulk to the walls, the mixture phase tends to phase separate ¯rst in vicinity of the walls, and then, deeper and deeper within the bulk. During this process, convection may arise, due to the above mentioned non equilibrium reversible body force, thus enhancing heat transport and, in particular increasing the heat °ux at the walls [D. Molin, and R. Mauri, "Enhanced Heat Transport during Phase Separation of Liquid Binary Mix- tures," Phys. Fluids 19, 074102-1-10 (2007)]. The model has been extended then and applied to the case where the two phases have di®erent heat con- 3 ductivities. We saw that heat transport depends on two parameters, the Lewis number and the heat conductivity ratio. In particular, varying these parameters can a®ect the orientation of the domains that form during phase separation. Domain orientation has been parameterized using an isotropy coe±cient », varying from -1 to 1, with » = 0 when the morphology is isotropic, » = +1 when it is composed of straight lines along the transversal (i.e. perpendicular to the walls) direction, and » = ¡1 when it is composed of straight lines along the longitudinal (i.e. parallel to the walls) direction [D. Molin, and R. Mauri, "Spinodal Decomposition of Binary Mixtures with Composition-Dependent Heat Conductivities," Int. J. Engng. Sci., in press (2007)]. In order to further extend the model, we removed the constraint of a constant viscosity, and simulated a well known problem of drops in shear °ows. There we found that, predictably, below a certain threshold value of the capillary number, the drop will ¯rst stretch and then snap back. At lager capillary numbers, though, we predict that the drop will stretch and then, eventually, break in two or more satellite drops. On the other hand, applying traditional °uid mechanics (i.e. with in¯nitesimal interface thick- ness) such stretching would continue inde¯nitely [D. Molin and R. Mauri, " Drop Coalescence and Breakup under Shear using the Di®use Interface Model," in preparation]. Finally, during a period of three months at the Eindhoven University, we extended the DI model to a three component °uid mixture, using a di®erent form of the free energy, as derived by Lowengrub and Coworkers.. With this extension, we simulated two simple problems: ¯rst, the coalescence/repulsion of two-component drops immersed in a third component continuum phase; second, the e®ect of adding a third component to a separated two phase system. Both simulations seem to capture physical behaviors that were observed experimentally [D. Molin, R. Mauri and P. Anderson, " Phase Separation and Mixing of Three Component Mixtures," in preparation]

Predicting and controlling bubble clogging in bioreactor for bone tissue engineering

A common problem in small scale bioreactors like those used for tissue engineering is the clogging of microchannels by gas bubbles. In case of clogging, the flow distribution inside the bioreactor changes and can not guarantee the adequate transport of nutrients and efficient removal of catabolites. Bubbles may (i) enter with the flow during the priming phase, when the reactor is first filled with the culturing medium, or may (ii) form locally during operations, because of gas desorption from scaffold, intense cellular metabolic activity or degassing. In this work, we develop and use an analytical model to identify the conditions (bioreactor region, flow rate, limiting bubble size) for which bubbles may adhere stably to the scaffold, potentially leading to bubble clogging. Based on the flow and shear stress distribution calculated by numerical simulation, the model indicates that clogging may occur in the region around the scaffold and along scaffold channels. Operative conditions under which clogging can be avoided are identified

Turbulence modulation and microbubble dynamics in vertical channel flow

In this paper we examine the mutual interactions between microbubbles and turbulence in vertical channel flow. An Eulerian-Lagrangian approach based on pseudo-spectral direct numerical simulation is used: bubbles are momentum coupled with the fluid and are treated as pointwise spheres subject to gravity, drag, added mass, pressure gradient, Basset and lift forces. Two different flow configurations (upward and downward channel flow of water at shear Reynolds number Re-tau = 150) and four different bubble diameters are considered, assuming that bubbles are non-deformable (i.e. small Eotvos number) and contaminated by surfactants (i.e. no-slip condition applies at bubble surface). Confirming previous knowledge, we find macroscopically different bubble distribution in the two flow configurations, with lift segregating bubbles at the wall in upflow and preventing bubbles from reaching the near-wall region in downflow. Due to local momentum exchange with the carrier fluid and to the differences in bubble distribution, we also observe significant increase (resp. decrease) of both wall shear and liquid flowrate in upflow (resp. downflow). We propose a novel force scaling to examine results in vertical turbulent bubbly flows, which can help to judge differences in the turbulence features due to bubble presence. By examining two-phase flow energy spectra, we show that bubbles determine an enhancement (resp. attenuation) of energy at small (resp. large) flow scales, a feature already observed in homogeneous isotropic turbulence. Bubble-induced flow field modifications, in turn, alter significantly the dynamics of the bubbles and lead to different trends in preferential concentration and wall deposition. In this picture, a crucial role is played by the lift force, which is a delicate issue when accurate models of shear flows with bubbles are sought. We analyze and discuss all the observed trends emphasizing the impact that the lift force model has on the simulations

Unified framework for a side-by-side comparison of different multicomponent algorithms: Lattice Boltzmann vs. phase field model

Lattice Boltzmann models (LBM) and phase field models (PFM) are two of the most widespread approaches for the numerical study of multicomponent fluid systems. Both methods have been successfully employed by several authors but, despite their popularity, still remains unclear how to properly compare them and how they perform on the same problem. Here we present a unified framework for the direct (one-to-one) comparison of the multicomponent LBM against the PFM. We provide analytical guidelines on how to compare the Shan–Chen (SC) lattice Boltzmann model for non-ideal multicomponent fluids with a corresponding free energy (FE) lattice Boltzmann model. Then, in order to properly compare the LBM vs. the PFM, we propose a new formulation for the free energy of the Cahn–Hilliard/Navier–Stokes equations. Finally, the LBM model is numerically compared with the corresponding phase field model solved by means of a pseudo-spectral algorithm. This work constitute a first attempt to set the basis for a quantitative comparison between different algorithms for multicomponent fluids. We limit our scope to the few of the most common variants of the two most widespread methodologies, namely the lattice Boltzmann model (SC and FE variants) and the phase field model