focus on Chromatography
The Effects of Bead Overlap on Performance of 3D Printed Packed Bed Columns
Suhas Nawada, Simone Dimartino, Conan Fee, Department of Chemical & Process Engineering and Biomolecular Interaction Centre, University of Canterbury, Private Bag 4800, Christchurch 8041, New Zealand
We propose the use of 3D printing as a production method for chromatography columns with precise control over particle size, shape, orientation and placement. In this paper, we introduce the concept of overlapping beads for structural stability and create columns with differing degrees of bead overlap, leading to different extra-particle porosities. Geometrical analysis and residence time distribution studies have shown that the experimental porosities were consistent with the designed porosity of the columns. This study demonstrates the fi ne control of packing features that 3D printing can offer in the fi eld of chromatography.
, or η = 0.636 random close packing (RCP), is generally considered to be the upper limit both in terms of packing density and performance in packed bed chromatography. The particle shape, size and orientation are a by-product of the physico-chemical properties of the stationary phase as well as the slurry packing procedure [1, 2]. Because no two randomly packed confi gurations are identical, predictions of column performance have relied on empirical models, rather than an a-priori consideration of the exact packed bed geometries.
The column preparation process has traditionally involved ‘jam-packing’ columns to the maximum packing density that is possible with slurry packing. A mathematical limit of packing density η = π
2
The two major parameters that are used to predict column performance are extra-particle porosity and a shape factor used in the Darcy, Karman, Cozeny and Ergun equations. Extra-particle porosity is often used as a rule of thumb to describe the packed bed homogeneity, tortuosity and, in combination with the particle diameter, internal surface area. Because these four parameters are interdependent in the case of random packing, it has been impossible to isolate any single geometric parameter for further study.
Equations predicting the height equivalent theoretical plates (HETP) require a term for ‘packing quality’, an all-encompassing term to describe packing heterogeneity, any structural defects in the packing and particle shape and size distributions. The packing quality is determined post-hoc in the form of band broadening. The van Deemter equation, for example, has been found to fi t experimental data on plate heights with good accuracy. However, this does not necessarily mean that the effects of packing geometry on HETP are well understood. To quote Gritti et. al. “Despite this good fi t, it is generally recognised that the best parameters provided by this mathematical exercise are purely empirical and void of physical sense” [3].
Because of diffi culties in controlling the exact positioning of beads in packed beds, efforts to investigate packing geometry have been limited to computational studies, without experimental validation. Simulations used to study random packed columns have traditionally relied on iterative algorithms such as the Jodrey-Tory, Monte Carlo or Lubovchesky-Stillinger algorithms to produce the packing arrangements [4]. While it is possible to achieve the theoretical RCP limits and control several important geometric parameters using these algorithms, it has not been possible to recreate the exact packed bed geometries that the slurry packing process produces. The algorithms assume, for the sake of mathematical simplicity, that the particles are perfectly spherical and identical in shape and size, in contrast to the case in actual chromatography columns, which are known to have beads of varying shapes and a range of particle sizes. While CFD studies have shown the effects of several key packing parameters on band-broadening, a disconnect between the computational and experimental studies has remained.
One approach to avoid the problems faced in random packing would be to produce chromatography columns with an ordered lattice of beads. Apart from achieving optimal packing arrangements and lower extra-particle porosities, this approach would eliminate the band broadening associated with random packing. In addition, traditional empirical models of chromatographic performance would be challenged, because extra-particle porosity does not automatically serve as an indicator of packing quality and tortuosity in the case of ordered packing. For example, it has been shown in computational studies that the traditional three-parameter van Deemter model does not predict plate heights for several ordered packing arrangements [5]. However, while an ordered packing geometry
Figure 1. Comparison of non overlapping (a) and overlaying (b) octahedral beads.
has been produced at a capillary scale [6], it has been impossible to produce an ordered arrangement of particles at a scale that is relevant to FPLC systems.
In this study, we used the process of 3D printing, or additive manufacturing, to produce packed beds with control over the placement, size, shape and orientation of each particle [7]. Computer aided design (CAD) models of the entire column, including the packed bed, column walls, fl uid distributors and end fi ttings can be designed and produced as a one- piece system. Using 3D printing, it is possible for the fi rst time to create a perfectly ordered bead arrangement at a large scale. It is also not necessary, as we show in this paper, to limit ourselves to spherical or randomly shaped beads because it is possible to design and create particles of any shape, as long as the resolution of the 3D printer is adequate.
To maintain the structural stability of the packing, a certain amount of overlapping of the beads is necessary. As Figure 1 shows, a packing where only the vertices of the beads are in contact is unlikely to maintain its packing confi guration over time. To ensure the packing elements maintain a constant spatial confi guration over time, even under mechanical stress, the packing elements need to be securely joined one another by overlaying their vertexes. Such overlap also serves as a tool to gain further insights into the effects of packed bed microstructure on chromatographic performance. In random packing, porosity serves as a reliable predictor of other packing parameters such as tortuosity, internal surface area and packing quality and heterogeneity. In the case of ordered packing, particle shape and packing confi guration determine the porosity, the surface area as well as the characteristic shape of the voids through which the mobile phase fl ows. In addition to shape and orientation, these structural parameters can be appropriately tuned if particle overlap is considered among the design variables to generate the packing morphology.
The goal of the present paper was to assess the quality of 3D printed columns designed with different bead overlaps (Table 1). Porous lattices with varying degrees of bead overlap were fi rst designed and then manufactured by 3D printing. The quality of the printed models was evaluated through optical microscope images, while the fl ow performance of the columns obtained was tested using residence time distribution experiments.
INTERNATIONAL LABMATE - APRIL 2014
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