On the compact wave dynamics of tensegrity beams in multiple dimensions

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams reveal - for the first time - the presence of compact compression waves in two- and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices

On shear and torsion factors in the theory of linearly elastic rods

Lower bounds for the factors entering the standard notions of shear and torsion stiffness for a linearly elastic rod are established in a new and simple way. The proofs are based on the following criterion to identify the stiffness parameters entering rod theory: the rod's stored-energy density per unit length expressed in terms of force and moment resultants should equal the stored-energy density per unit length expressed in terms of stress components of a Saint-Venant cylinder subject to either flexure or torsion, according to the case. It is shown that the shear factor is always greater than one, whatever the cross section, a fact that is customarily stated without proof in textbooks of structure mechanics; and that the torsion factor is also greater than one, except when the cross section is a circle or a circular annulus, a fact that is usually proved making use of Saint-Venant's solution in terms of displacement components.Comment: 1 figur

A 2D metamaterial with auxetic out-of-plane behavior and non-auxetic in-plane behavior

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance, two-dimensional bodies have more freedom to deform than three-dimensional ones. Here, we exploit this peculiarity and propose a two-dimensional honeycomb structure with out-of-plane auxetic behavior opposite to the in-plane one. With a suitable choice of the lattice constitutive parameters, in its continuum description such a structure can achieve the whole range of values for the bending Poisson coefficient, while retaining a membranal Poisson coefficient equal to 1. In particular, this structure can reach the extreme values, $-1$ and $+1$, of the bending Poisson coefficient. Analytical calculations are supported by numerical simulations, showing the accuracy of the continuum formulas in predicting the response of the discrete structure

A Class of Minimal Generically Universally Rigid Frameworks

Following a review of related results in rigidity theory, we provide a construction to obtain generically universally rigid frameworks with the minimum number of edges, for any given set of n nodes in two or three dimensions. When a set of edge-lengths is compatible with only one configuration in d-dimensions, the framework is globally rigid. When that configuration is unique even if embedded in a higher dimensional space, the framework is universally rigid. In case of generic configurations, where the nodal coordinates are algebraically independent, the minimum number of edges required is equal to dn-d(d+1)/2+1, that is, 2n-2 for d=2, and 3n-5 for d=3. Our contribution is a specific construction for this case by introducing a class of frameworks generalizing that of Gr\"{u}nbaum polygons. The construction applies also to nongeneric configurations, although in this case the number of edges is not necessarily the minimum. One straightforward application is the design of wireless sensor networks or multi-agent systems with the minimum number of communication links.Comment: 8 page

Appraisal of microcarrier suspension dynamics in shaken bioreactors

The pharmaceutical industry is at the forefront of the production of drug products using mammalian cell-based cultures, some of which rely on adherent-dependant cells. Whilst often adapted to suspension cultures, hybridoma and other cells give increased product yields when cultured attached to a substrate, such as microcarriers, resulting in smaller fermentation runs at higher densities. Microcarriers are also used in tissue engineering and cell for therapy culture. Stem cells are adherent-dependant cells and traditional 2-dimensional static cultures rely on disposable multilayer vessels, which have become the common route for stem cell expansion, although remain labour and handling intensive. Large scale production of stem cells would require the use of 3-dimensional dynamic culture methods by employing microcarrier technology, as demonstrated by Frauenschuh et al. (2007). Microcarriers consist of spherical beads with a size of 100-300 μm, and can be made of a wide variety of materials, some of them biodegradeable. Whilst most studies have focused on investigating optimal compositions of microcarrier materials, their concentration and cell culture media, little research has been undertaken on the engineering aspects of microcarrier use, such as the just-suspended speed and suspension quality. The aim of the work is to characterize the suspension dynamics of microcarriers in a cylindrical orbitally shaken bioreactor (OSR) with conical bottoms of different heights. The proposed conical bottom geometry has been proven to provide enhanced vorticity when compare to a flat bottom vessel (2). This study builds upon previous works of the research group 3-6) for a flat bottom reactor, where increases in Froude number were found to determine a mean flow transition which was found to be instrumental in determining the just-suspended speed. The dynamics of solid suspension is studied using commercially available Cytodex-3, stained with trypan for improved visual contrast. Image acquisition and computer image processing is employed to objectively measure suspension. The experimental procedure allows estimating not only the speed required for the solids to lift from the vessel bottom, but also the conditions at which a homogenous distribution of microcarriers is obtained. Preliminary results indicate that the presence of the conical bottom improves solid suspension by requiring lower agitation rates for the microcarriers to lift from the bottom completely. The critical Froude, which determines the flow type controlling the bioreactor, can be used to scale the suspension of microcarriers in OSRs. The suspension results are corroborated by mixing time measurements performed using the Dual Indicator System for Mixing Time (4), which show enhanced global mixing times when a conical bottom geometry is employed. 1. Frauenschuh, S., E. Reichmann, Y. Ibold, P. M. Goetz, M. Sittinger, and J. Ringe. A microcarrier-based cultivation system for expansion of primary mesenchymal stem cells. Biotechnology progress 2007,23,187–193. 2. Rodriguez G, Anderlei T, Micheletti, M, Ducci A Appraisal of fluid flow in a shaken bioreactor with conical bottom at different operating conditions, Chem Eng Res Des. 2016;108;186-197 3. Rodriguez G, Weheliye W, Anderlei T, Micheletti M, Yianneskis M, Ducci A. Mixing time and kinetic energy measurements in a shaken cylindrical bioreactor. Chem Eng Res Des. 2013;81:331–341. 4. Weheliye W, Yianneskis M, Ducci A. On the fluid dynamics of shaken bioreactors - flow characterization and transition. AIChE J. 2013;59:334–344. 5. Rodriguez G, Anderlei T, Micheletti M, Yianneskis M, Ducci A. On the measurement and scaling of mixing time in orbitally shaken bio- reactors. Biochem Eng J. 2014;82:10–21. 6. Pieralisi I, Rodriguez G., Micheletti M., Paglianti A., Ducci A. Microcarriers’ suspension and flow dynamics in orbitally shaken bioreactors. Chem Eng Res Des. 2016; 108;198-209

Study on mixing and fluid dynamics in single-use shaken systems

Bioreactors are widely used in a range of applications, including the food/drink, pharmaceutical and medical industries. Stirred Tank Reactors (STRs) are the most widely used and rely on mechanical stirrers to achieve the optimal fluid motion, and their flow dynamics has been extensively studied for a broad combination of operating conditions (Ducci and Yianneskis 2005, 2007, Escudie and Line 2003). Orbitally Shaken Reactors (OSRs) promote agitation through the orbital motion of the bioreactor, which induces sloshing of the free surface. Their flow dynamics has been mainly assessed for lab scale reactors of cylindrical cross-section, while few studies in terms of mixing and fluid dynamics are available for unconventional shapes at limited scales. During early stages of bioprocess development, single-use ml-scale shaken multi-well plates are commonly used for scale-down studies as they allow a large number of experiments to be performed using small amounts of material. However, very few studies published on shaken bioreactors have thoroughly studied the engineering aspects and the hydrodynamics at such a small scale, thus resulting in a lack of accurate scaling correlations between shaken and large scale conventional bioreactors. The flow in orbitally shaken reactors has been characterised by Weheliye et al (2013) and Ducci and Weheliye (2014) and a scaling law has been developed for two cylindrical reactors with internal diameters of 10 and 13 cm. However, the understanding of reactors with square shape is still very limited despite they have a number of practical applications. For example, two different disposable shaken reactors with square cross-sections have been used by Stettler et al (2007) for transient gene expression. The aim of this work was twofold – (i) to estimate the mixing time in microwell plates of different geometry and determine an effective scaling parameter between micro-scale and lab-scale reactors and (ii) to determine the fluid dynamics in square reactors and identify analogies with baffled stirred tanks. In the first part of this study, mixing time was measured in microscale systems by adopting the Dual Indicator System for Mixing Time (DISMT) method, and the effects of fill volume, fluid viscosity and surface tension were investigated in 24-DSW and cylindrical geometries on a ThermoMixer with orbital diameter of 3 mm. The mixing time of the DSW showed in general the typical variation of a mixing number curve, however it was identified a range of rotational speed N=600-650 rpm, which was denoted by an increase of mixing time with speed. This phenomenon is caused by a reduced free surface oscillation over this range of speeds, which does not occur when a cylindrical geometry is considered. With a reduction of surface tension this phenomenon disappears also in the deep square wells. Mixing time measurements were also carried out in intermediate-sized reactors and compared to those obtained in lab-scale reactors by Rodriguez et al (2013, 2014). These data indicate that the natural frequency of a filled container can be used as an effective parameter to scale between microwells and larger scale shaken reactors. Secondly, Horizontal PIV measurements were carried out in a squared shaken bioreactor with a diameter of 6.2 cm, which has the same cross-sectional area as the cylindrical reactor used by Rodriguez et al (2014). The flow in a square OSR is clearly different from what have been observed in cylindrical reactors previously. All the ensemble averaged velocity fields obtained in the square tank for a range of rotational speeds shown the effect of the four corners on fluid flow. The directions of the flow at a few phase angles were also investigated by phase-resolved PIV measurements and they were found in agreement with the flow directions in cylindrical shaken reactors. The average of the kinetic energy of a lower plane is smaller than that for a higher plane and the kinetic energy distribution also demonstrated the effects of the presence of four corners on the flow inside the square reactor. Ducci and Weheliye (2014) AIChE J., 60(11): 3951-3968. Ducci and Yianneskis (2005) AIChE J., 51(8): 2133-2149. Ducci and Yianneskis (2007) AIChE J., 53(2): 305-315. Escudie and Line (2003) AIChE J., 49: 585-603. Rodriguez et al (2013) ChERD, 91: 2084-2097. Rodriguez et al (2014) BEJ, 82: 10-21. Stettler et al (2007) BP., 23: 1340-1346. Weheliye et al (2013) AIChE J., 59(1): 334-344

Fluid dynamics in a novel single-use bioreactor for personalised T-cell therapies

The complex nature of advanced personalised therapies requires the development of an incredibly robust manufacturing process that yields consistent final product quality despite patient-to-patient variability. Therefore, a lot of effort is focused on the design of novel, fully automated platforms that can accommodate the whole bioprocess in one closed system, using one or more single-use components. Please click Additional Files below to see the full abstract