Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Department of Chemical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India
Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
Author to whom correspondence should be addressed.
Received: 13 February 2019 / Revised: 2 March 2019 / Accepted: 5 March 2019 / Published: 11 March 2019
We combine a slip-spring model with an ‘entangled kink dynamics’ (EKD) model for strong uniaxial extensional flows (with Rouse Weissenberg number
) of long (
for polystyrene) entangled polymers in solutions and melts. The slip-spring model captures the dynamics up to the formation of a ‘kinked’ or folded state, while the kink dynamics simulation tracks the dynamics from that point forward to complete extension. We show that a single-chain slip-spring model using affine motion of the slip-spring anchor points produces unrealistically high tension near the center of the chain once the Hencky strain exceeds around unity or so, exceeding the maximum tension that a chain entangled with a second chain is able to support. This unrealistic tension is alleviated by pairing the slip links on one chain with those on a second chain, and allowing some of the large tension on one of the two to be transferred to the second chain, producing non-affine motion of each. This explicit pairing of entanglements mimics the entanglement pairing also used in the EKD model, and allows the slip spring simulations to be carried out to strains high enough for the EKD model to become valid. We show that results nearly equivalent to those from paired chains are obtained in a single-chain slip-spring simulation by simply specifying that the tension in a slip spring cannot exceed the theoretical maximum value of
are the friction per unit length, strain rate and contour length of the chain, respectively. The effects of constraint release (CR) and regeneration of entanglements is also studied and found to have little effect on the chain statistics up to the formation of the kinked state. The resulting hybrid model provides a fast, simple, simulation method to study the response of high molecular weight (
) polymers in fast flows (
), where conventional simulation techniques are less applicable due to computational cost.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Moghadam, S.; Saha Dalal, I.; Larson, R.G. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers 2019, 11, 465.
Moghadam S, Saha Dalal I, Larson RG. Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids. Polymers. 2019; 11(3):465.
Moghadam, Soroush; Saha Dalal, Indranil; Larson, Ronald G. 2019. "Slip-Spring and Kink Dynamics Models for Fast Extensional Flow of Entangled Polymeric Fluids." Polymers 11, no. 3: 465.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.