# Current Limitations for Predicting Liquid Dispersion in Continuous Flow Bubble Columns Using CFD
## 1 Introduction  
A bubble column is typically a vertical cylindrical vessel with a continuous liquid phase and a dispersed gas phase. Bubble columns are widely used for gas-liquid reactions because of their simplicity and ability to achieve good interphase mass transfer [1; 2; 3]. Geometric factors (column diameter and height, features of the gas sparger), the properties of fluids, and flow rates of the gas and liquid phases influence important operational characteristics such as gas holdup (volume fraction of gas in gas-liquid dispersion) and gas-liquid interfacial area for mass transfer in bubble columns [1; 2; 3; 4; 5]. Although simple in geometric configuration, bubble columns are characterized by a complex two-phase flow [6; 7]. The flow in a bubble column is influenced by the movement of the gas bubbles, which in turn depends on their size and size distribution and on gas holdup [8]. The random movement of bubbles, bubble coalescence and breakup, and interaction with the column walls, create complex turbulence patterns that can be difficult to predict. Different flow regimes and extents of backmixing (mixing along the axial direction) are desirable in bubble columns for different applications [9]. Some processes require high superficial velocities of phases to achieve a highly turbulent heterogenous flow regime to support the required rates of mass transfer and reaction [10; 11; 12]. In other cases, much lowerflow velocities are satisfactory and actually desired to minimize the energy input and the turbulence-associated damage to biological systems [13]. Different aspects of the performance of a bubble column are characterized in terms of gas holdup, the axial and radial liquid-phase dispersion coefficients, and gas-liquid volumetric mass transfer coefficients [1; 2; 3; 5]. Many empirical correlations have been developed for estimating these performance characteristics in different media and flow regimes [1; 2; 3; 5; 14]. The mixing caused by the convective motion of fluids in a bubble column has axial and radial components. Axial and radial dispersion coefficients are used to characterize this mixing. The dispersion coefficients are analogous to the diffusion coefficients of [PERSON]'s law [15]. In bubble columns operated batchwise with respect to the liquid phase, mixing is often characterized in terms of a mixing time, or the time required to achieve a specified deviation (e.g., 5%) from the state of complete mixedness (equilibrium concentration) after the injection of a tracer [16]. Continuous-flow bubble columns are characterized by the transient response of the tracer concentration [17]. Computational fluid dynamics (CFD) provides a valuable tool for describing local physical phenomena encountered in bubble column flows and, therefore, quantitatively predicting the behavior of the phases [18]. Accurate predictions are possible by using direct numerical simulation (DNS) instead of simplifying models, but this would require supercomputing facilities, especially for large columns [19]. Although computationally demanding in terms of hardware power, biphasic models based on Euler-Lagrange (E-L), such as volume of fluid (VOF), provide a clear physical description of particle movement (e.g., gas bubble), or fluid flow, and therefore are expected to become the norm in modeling flow in the future as more powerful computers become more readily accessible. At present, because of the computational demands of E-L models, studies based on them have been limited to small-sized equipment that is not particularly relevant to large-scale industrial operations. Therefore, most of the current two-phase CFD studies have used Euler-Euler (E-E) modeling schemes [20]. The VOF model and the E-E two-fluid model are very different models. In the VOF model, a single flow field is used to describe the two phases and solve a single set of flow and energy equations. Interfacial forces exist in the interface layer and act as a source term in the Navier-Stokes (N-S) equations (only one vector equation for the two-phase flow).