Two-dimensional hydrodynamics of a Janus particle vesicle

Abstract

We develop a new model, to our knowledge, for the many-body hydrodynamics of amphiphilic Janus particles suspended in a viscous background flow. The Janus particles interact through a hydrophobic attraction potential that leads to self-assembly into bilayer structures. We adopt an efficient integral equation method for solving the screened Laplace equation for hydrophobic attraction and for solving the mobility problem for hydrodynamic interactions. The integral equation formulation accurately captures both interactions for near touched boundaries. Under a linear shear flow, we observe the tank-treading deformation in a two-dimensional vesicle made of Janus particles. The results yield measurements of intermonolayer friction, membrane permeability and, at large shear rates, membrane rupture. The simulation studies include a Janus particle vesicle in both linear and parabolic shear flows, and interactions between two Janus particle vesicles in shear and extensional flows. The hydrodynamics of the Janus particle vesicle is similar to the behaviour of an inextensible, elastic vesicle membrane with permeability.

Effects of Tunable Hydrophobicity on the Collective Hydrodynamics of Janus Particles under Flows

“…Pure lipid components give a range of interfacial tensions 0.7-5.3 pN nm −142-45 . As in our previous works 17,18 , we use 𝛾 = 4.1 pN nm −1 since this value gave good agreement with elastic moduli of lipid bilayers. The particle radius 𝑐 = 1.25 nm gives a diameter representative of phospholipid length 41 , and the screening length 𝜌 = 5 nm derives from experimental force-distance measurements of hydrophobic attraction [31][32][33]44 .…”

“…Following the formulation in Fu et al 18 , the governing equations are expressed as a system for the position and orientation of a collection of rigid Janus particles. We first pose the Stokes equations for the mobility problem giving the hydrodynamic interactions for the particle suspension.…”

“…This means that the force and torque from the hydrodynamic stress on each particle balance the total force and torque coming from the hydrophobic potential and repulsion. To compute this balance, we define the free energy 17,18,29,30 𝐹 = 𝛾…”

“…The many-body hydrodynamics of amphiphilic Janus particles assembled as vesicles suspended in a viscous fluid in the inertialess regime (zero Reynolds number) has been studied using boundary integral numerical simulations 17,18 . The dynamics of the JP suspension results from the combination of long-range hydrodynamic interaction and non-local interactions between JPs through the distribution of a hydrophobic attraction potential (HAP).…”

“…In a quiescent flow, numerical simulations of a JP suspension showed self-assembly into micelles and bilayers of JPs that provide an alternative means for computing the mechanical moduli of a colloidal membrane 17,19,20 . Under background flows, the hydrodynamics of a JP vesicle (a self-enclosed bilayer of JPs) exhibit many familiar behaviors of a vesicle: elongation and alignment along the extensional direction, tank-treading, and rupture of a vesicle under shear flow 18,[21][22][23][24][25] .…”