Using Brownian dynamics simulations to demystify capillary breakup extensional rheometry (CaBER)

Difficulties in extracting rheological properties from capillary breakup extensional rheometry (CaBER) are addressed by using Brownian dynamics (BD) simulations of bead-spring polymer chains with finite extensibility (FE), excluded volume (EV), and hydrodynamic interactions (HIs), coupled with a simplified multistage description of flow kinematics. The deformation dependence of HIs is modeled by the approximate “C2D2” model [Prabhakar et al., Phys. Rev. Fluids 2(1), 011301 (2017)], which uses a stretch- and concentration-dependent bead-drag coefficient, thereby avoiding the unmanageably large expense of solving the BD equations with the Rotne–Prager tensor for long chains that influence each other hydrodynamically. We validate our simulations with literature data for polyethylene oxide solutions in both step strain and slow retraction CaBER. We obtained the kinematics of CaBER by combining an analytical early time viscous solution for the filament radius versus time for Newtonian filaments with a later-time balance of capillary stress, viscous stress, and polymer stress. The polymer stress is derived from BD simulations, updating the extension rate as a function of time using the stress balance. The success of this method allows us to clarify the complex relationship between the longest equilibrium polymer relaxation time τZ and the apparent relaxation time τa inferred from the CaBER fiber diameter using D(t)∝exp(−t/3τa) in the regime of exponential decay of diameter with time. We find computationally that τa can be either greater than or less than τZ since FE reduces τa and HI increases it, to extents that depend on molecular weight, polymer concentration, endplate radii, and endplate separation protocol. Maps of EV, FE, and HI dependencies, molecular weight, and the size of endplate diameter relationship are presented, which helps clarify the rheology measured by CaBER and provides rules of thumb to interpret the data extracted from CaBER for experimentalists.