{'fraction_non_alphanumeric': 0.013195098963242224, 'fraction_numerical': 0.0, 'mean_word_length': 5.138728323699422, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Constitutive equation for electrorheological fluids based on the chain model

Electrorheological fluids show a dramatic increase in flow resistance under an electric field. For the case of simple shear flow, a microstructural model that has been extensively used to date is the chain model, whereby the increased shear viscosity is attributed to the chain-like aggregates of particles which form due to the interactions between the induced electric dipoles in the particles. In this paper, the model is extended to the case of a general flow field described by the velocity gradient tensor καβ, to produce a general constitutive framework. The orientation and length of the chains are determined from the balance of the electric torque, which acts to align each chain with the electric field, and the hydrodynamic torque, which tends to rotate each chain in the imposed flow field. This formulation is used to calculate the stress tensor for flow fields and electric fields with different geometries, and the results show qualitative agreement with experiments.