Negative synergistic effects of surfactant and fluid viscoelasticity on hydrodynamic resistance of single droplet in confined microchannel

Polymers and surfactants are often employed simultaneously to control droplet dynamics with higher flexibility in many applications, such as droplet microfluidics and chemical enhanced oil recovery. However, the coupling effects of polymer-induced fluid viscoelasticity and surfactant have not been fully uncovered yet. To facilitate studies in this area, we present a systematic investigation on the transport of a surfactant-laden viscoelastic droplet through a confined microchannel by using our own three-dimensional front-tracking finite-difference methodology. Of particular interest is the droplet-induced additional pressure loss, which is important to deeply understand the flow rate-pressure loss relation of droplet-laden flows. We have found that either the fluid viscoelasticity or surfactant tends to enlarge the additional pressure loss, while their co-occurrence induces a further increase. Notably, negative synergistic effects are indicated between fluid viscoelasticity and surfactant; that is, their combined effect to increase the additional pressure loss is smaller than the sum of their individual effects. This synergistic effect primarily results from mutual inhibition of the viscoelastic stress and the surfactant-induced Marangoni stress to reduce the droplet surface mobility, no matter whether the surfactant is soluble or insoluble. Particularly, when the surfactant is soluble to the viscoelastic fluid phase, its transport and the consequent Marangoni stress is suppressed by the bulk viscoelastic stress via two mechanisms: the weakened surface convection by direct impact of the viscoelastic stress on the droplet surface mobility and the weakened bulk convection by the flow modification effect.