Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical approximation of a phase-field surfactant model with fluid
  flow   Modelling interfacial dynamics with soluble surfactants in a multiphase
system is a challenging task. Here, we consider the numerical approximation of
a phase-field surfactant model with fluid flow. The nonlinearly coupled model
consists of two Cahn-Hilliard-type equations and incompressible Navier-Stokes
equation. With the introduction of two auxiliary variables, the governing
system is transformed into an equivalent form, which allows the nonlinear
potentials to be treated efficiently and semi-explicitly. By certain subtle
explicit-implicit treatments to stress and convective terms, we construct first
and second-order time marching schemes, which are extremely efficient and
easy-to-implement, for the transformed governing system. At each time step, the
schemes involve solving only a sequence of linear elliptic equations, and
computations of phase-field variables, velocity and pressure are fully
decoupled. We further establish a rigorous proof of unconditional energy
stability for the first-order scheme. Numerical results in both two and three
dimensions are obtained, which demonstrate that the proposed schemes are
accurate, efficient and unconditionally energy stable. Using our schemes, we
investigate the effect of surfactants on droplet deformation and collision
under a shear flow, where the increase of surfactant concentration can enhance
droplet deformation and inhibit droplet coalescence.

13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat