Predicting the diameters of droplets produced in turbulent liquid–liquid dispersion

Abstract

The droplet size distribution in liquid-liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier-Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events.In the second approach, based on an Eulerian-Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian-Parcel model, we model a sub-set of the droplets in the Eulerian-Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.

CFD‐based bioreactor model with proportional–integral–derivative controller functionality for dissolved oxygen and pH

“…As a bubble moves through the fluid, its diameter will change due to break‐up, coalescence, changes in local hydrostatic pressure, and mass exchange with the surrounding fluid. Bubble break‐up occurs when the local EDR of the fluid surrounding a bubble exceeds the bubble surface energy (Thomas, DeVincentis, et al, 2021). The diameter of the largest bubble stable against break‐up can be estimated from first‐principles turbulence theory (Hinze, 1955).…”

“…This distribution function is then sampled to evaluate the volume fraction of the daughter bubbles. At EDRs relevant to this work (<1000 W/kg), this daughter volume distribution is typically M‐shaped with a minimum at 0.5 and maxima at 0.1 and 0.9 (Thomas, DeVincentis, et al, 2021; Xing et al, 2015). Bubble coalescence and bubble bounce events are distinguished using the bubble pair Reynolds number (Boshenyatov, 2013).…”

Modeling multiphase fluid flow, mass transfer, and chemical reactions in bioreactors using large‐eddy simulation

“…[12] Since these two governing equations are solved in tandem, changes in the species concentration can inform the local viscosity. We solve Equations ( 1) and ( 2) using the lattice-Boltzmann (LB) method ( 13), as discussed in detail in our previous reports (14)(15)(16)(17).…”

“…Bubble forces are (two-way) coupled via Newton's third law to the fluid through drag, density and added mass [19]. Bubble break-up and coalescence are handled at the level of individual bubbles and bubble pairs, as discussed in detail in our previous reports [15][16][17].…”

“…oxygen concentrations after 20 min of process simulation. We superimpose on these results the solution to Equations (15)(16)(17)(18)(19), evaluated using the ODE45 solver in Matlab with the simulation-predicted oxygen 𝑘 𝑙 𝑎 of 0.014 1/s as input to the solution. The reaction rates of the biomass, gluconic acid, and substrate predicted from the simulations are in good agreement with the ODE45 solution.…”