Hydroelastic scattering and trapping of microswimmers

Phase separation in aqueous biopolymer mixtures results in the formation of an interface, separating two aqueous bulk phases. The properties of that interface are key parameters to understand and predict phenomena, such as the phase-separation process and deformation of droplets in a flow field. In these processes, the structures and sizes of the morphologies depend on the balance between viscous and interfacial forces. Normally, one assumes that the interfacial tension is the only important parameter regarding the interfacial forces. However, we will show that in these water-in-water emulsions, bending rigidity and interfacial permeability also play an important role. Spinning drop experiments show that at long time scales the interface is permeable to both dissolved biopolymers and water. From droplet relaxation experiments, we could conclude that, for shorter time scales, water is the only ingredient that can diffuse through the interface. Due to this permeability, these methods cannot be used to calculate the interfacial tension accurately, without taking into account the permeability of the interface. Including the permeability, we give a full description for the relaxation time of deformed droplets. From this description, the interfacial tension and the permeability of the interface can be deduced simultaneously. We also incorporate the permeability and the bending rigidity into the description of the kinetics of phase separation. From this theoretical description, we predict four different regimes to occur in the phase-separation process depending on the size of the domains. For the scaling of the domain size with time, we find an exponent of (1)/(4) for bending- and permeability-dominated coarsening, an exponent of (1)/(3) for bending-dominated coarsening, an exponent of (1)/(2) for interfacial tension- and permeability-dominated coarsening, and an exponent of 1 for interfacial tension-dominated coarsening. The crossover between the different regimes depends on two different critical radii, R(c), equal to (2k/gamma)(1/2) and R(lambda), equal to etalambda(eff). Taking values for the interfacial properties, we find these critical radii to be larger than a micrometer, indicating that both bending rigidity and permeability are of importance during phase separation.

We study the elastic properties of homopolymer/homopolymer interfaces containing diblock copolymers by means of a theory of Gaussian fluctuations. The interfacial tension and the bending rigidity of the interface in the two-phase coexistence region are calculated from the power spectrum of capillary modes. Our theory shows that in the limiting case of a pure binary homopolymer mixture, while the interfacial tension increases monotonically with increasing χN (where χ is the Flory-Huggins parameter and N is the homopolymer molecular weight) the bending rigidity does not. The bending rigidity increases rapidly at first for small values of χN, but then decreases with further increase of χN. In the presence of diblock copolymers, the interfacial tension always decreases with increasing diblock copolymer volume fraction at a given χN. However, the bending rigidity can show either a decrease or an increase depending on χN and the ratio γ between the molecular weights of a diblock copolymer and that of a homopolymer. Our results for the surface pressure and the bending rigidity are further compared with results based on scaling arguments of wet polymer brushes.

We study the hard-sphere fluid in contact with a planar hard wall. By combining the inhomogeneous virial series with simulation results, we achieve a new benchmark of accuracy for the calculation of surface thermodynamics properties such as surface adsorption Γ and the surface free energy (or surface tension), γ. We briefly introduce the problem of choosing a position for the dividing surface and avoid it by proposing the use of alternative functions to Γ and γ that are independent of the adopted frame of reference. Finally, we present analytic expressions for the dependence of system surface thermodynamic properties on packing fraction, ensuring the high accuracy of the parameterized functions for any frame of reference. The proposed parametric expressions for both, Γ and γ, fit the accurate simulation results within the statistical error.

The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.

In this work, the liquid-vapor (γlv), solid-liquid (γsl), and solid-vapor (γsv) surface tensions, as well as the line tension (τ) of water confined between planar rigid walls modeled as graphene sheets, are calculated from a single molecular dynamics simulation. While γlv and γsl are explicitly evaluated far from the contact lines between the liquid, vapor, and solid regions, γsv is deduced. Following a thermodynamic approach based on the description of the free energy, the line tension is determined from the three surface tensions, the pressures of the liquid and vapor phases, and the derivative of the free energy with respect to the length supporting the contact line. This analysis shows that the line tension cannot be reduced solely to the excess energy associated with line contact deformations. By relating the thermodynamic variables to the total stress along the x-direction, the mechanical and thermodynamic approaches are found to be consistent. We show that the line tension of confined water is negative and that neither temperature nor the degree of confinement affects its sign, which is consistent with other published results obtained using different methods. The main advantage of this approach lies in the ability to determine the three surface tensions and the line tension from a single atomistic simulation.

We investigated the effect of surfactants on an interface between two kinds of liquids by molecular dynamics (MD) simulation. We adopted the simple bead-spring model with two atoms as the surfactants. We controlled the interfacial tension of the surfactant adsorbed on the interface by changing the bond length. Although the interface's structure changed depending on the magnitude of the interfacial tension, the interface was stable even under conditions where the interfacial tension was virtually zero. The Fourier spectrum of the fluctuations of the surface structure showed a crossover from q2 to q4 when the interfacial tension was almost zero, where q is the wavenumber. This crossover means that the bending rigidity is dominant for the restoring force when the surfactant molecules are sufficiently absorbed on the interface and the interfacial tension is almost zero, whereas the interfacial tension is dominant when the interfacial tension is a finite value.

Using equations for the interfacial properties for a two-phase multicomponent system, we present a new model for the interfacial tension and bending rigidity for liquid-liquid interfaces between semidilute polymer phases. Using this model, we calculate the interfacial thickness and the bending rigidity for two different gelatin/dextran systems and a gelatin/gum arabic system using experimentally determined values for the interfacial tension. The bending rigidity of such systems has been unaccessible experimentally until now. For the gelatin/dextran systems, which are both near-critical, the interfacial thickness is very large (1000 nm) close to the critical point, where the interfacial tension is very low. Further from the critical point, the interfacial thickness decreases to a value in the order of the size of the biopolymers (100 nm). For the gelatin/gum arabic system, which is off-critical, we found the interfacial thickness to be constant, in the order of the size of the biopolymers. For the gelatin/dextran systems, the scaling relation between the interfacial tension and the interfacial thickness was investigated. The exponents were found to be approximately 1.7 for the two systems, which is in agreement with the exponent 2 of the scaling relation ~ 1/2. The accompanying bending rigidities for these near-critical gelatin/dextran systems were found to be approximately constant, with a value of 500 kbT. The bending rigidity for the gelatin/gum arabic system, which is off-critical, was in the order of 25 kbT. These high values for both the interfacial thickness and the bending rigidity for the near-critical systems may be of significance for interface-related phenomena in aqueous phase-separated biopolymer mixtures, in particular in cases where the bending contributions dominate the stretching contributions to the interfacial energy.

A micrometer-sized giant vesicle is studied by extending from the inside by using dual-beam optical tweezers in order to measure mechanical properties such as bending rigidity and surface tension of the membrane. As a micrometer-sized vesicle is extended, its shape gradually changes from a sphere to a lemon-shape, and discretely the lemon-shape deforms into a shape of a tube beside a sphere or a lemon part. The surface tension and the bending rigidity of the lipid membrane are obtained from the measured force-extension curve. In the one-phase vesicle, it is found that the surface tension is increasing as the charged component increasing, but the bending rigidity remains almost constant. In the phase-separated vesicle, the characteristic deformation different from one in the one-phase vesicle has been observed.

Surfactant formulations are extensively being developed in the oil industry for Enhanced Oil Recovery (EOR) applications. Surfactants suitable for EOR will form an oil-brine microemulsion (µE) with ultra-low interfacial tension (IFT), necessary for high recovery factors. Experimental screening of surfactants, to identify suitable formulations for reservoir conditions, is a laborious and time consuming process. In this paper we demonstrate an alternative, and novel, molecular modeling approach which is suitable for predicting µE properties and calculating optimum conditions. The molecular modeling simulations are based on the recently developed Method of Moments (MoM). The µE physics underlying the MoM is briefly reviewed in this paper. In the MoM the bending properties of the interfacial surfactant film are calculated as moments of the lateral stress profile. At optimum salinity the zeroth and first moments of the lateral stress profile are zero and the IFT will reach a minimum. In addition to optimum salinity, the bending rigidity (stiffness) of the surfactant film is another interesting microstructure property. The bending rigidity determines the oil/brine domain size, solubilization and magnitude of the IFT. The bending rigidity is accessible in the MoM via the saddle-splay modulus κs, which is calculated as the second moment of the lateral stress profile. It is shown in the paper how the shape of the lateral stress profile depends on molecular properties of the surfactant and on salinity. MoM simulations were carried out using the coarse-grained Dissipative Particle Dynamics (DPD) method. This computational approach is highly scalable, while preserving the structural information of chemical components in the system. This makes the method useful while screening the wide design space of possible surfactant-oil-brine combinations. We will discuss the predictive technique and some validation examples of predicting optimum salinity for oil-brine micro-emulsions. We will then demonstrate the effect of surfactant structural parameters like chain length, cosolvent etc. on the optimum salinity of the microemulsions.

The hydrodynamic interactions between a sedimenting microswimmer and a solid wall have ubiquitous biological and technological applications. A plethora of gravity-induced swimming dynamics near a planar no-slip wall provide a platform for designing artificial microswimmers that can generate directed propulsion through their translation–rotation coupling near a wall. In this work, we provide exact solutions for a squirmer (a model swimmer of spherical shape with a prescribed slip velocity) facing either towards or away from a planar wall perpendicular to gravity. These exact solutions are used to validate a numerical code based on the boundary integral method with an adaptive mesh for distances from the wall down to 0.1 % of the squirmer radius. This boundary integral code is then used to investigate the rich gravity-induced dynamics near a wall, mapping out the detailed bifurcation structures of the swimming dynamics in terms of orientation and distance to the wall. Simulation results show that a squirmer may traverse the wall, move to a fixed point at a given height with a fixed orientation in a monotonic way or in an oscillatory fashion, or oscillate in a limit cycle in the presence of wall repulsion.

Statistical mechanical theories of spherical fluid interfaces are discussed in the context of fluids in contact with structureless walls. The thermodynamic route to the surface tension leads to a formula involving gradients of the external field, which is especially suited to the study of fluid-wall systems. The surface tension is found to be determined by the curvature dependence of the density in the region of the wall. For hard walls, potential distribution theory is used to obtain the exact relationship between the statistical mechanical surface tension expression and the grand potential. The accuracy of simple scaled particle theory calculations of the surface tension is estimated from predictions for the equation of state of pair potential fluids with hard core plus attractive tail interactions. Problems with the mechanical route to the curvature dependence of the surface tension are discussed. The planar wall and results for lower dimensionality are included in appendices.

This paper reports the axisymmetric motion of a viscous droplet or solid spherical particle with a slip-flow surface that moves perpendicular toward an orifice in a plane wall. The motion is studied in the quasi-steady limit under a low Reynolds number. To maintain the spherical shape of the droplet, we assumed that the interfacial tension is very large. The radius of the droplet/particle may be either smaller or larger than the radius of the orifice. A general solution is established from fundamental solutions in both spherical and cylindrical coordinate systems. A semi-analytical approach based on dual integral equations and a collocation scheme is used. Numerical results show that the normalized drag coefficient acting on the droplet/particle is obtained with good convergence for different values of slip parameter, viscosity ratio, and spacing parameters. The findings demonstrate that the collocation results of the drag coefficient are consistent with the limiting cases available in the literature.

We perform a series of Monte Carlo simulations on an interface between a liquid crystal (LC) material in isotropic phase in its bulk and a surfactant membrane. These two objects are simulated using coarse-grained molecular models. We estimate physical properties of the membrane such as the interfacial tension and the bending rigidity, focusing on the anchoring effects of the membrane on the LC. According to our simulation results, when the strength of the homeotropic anchoring denoted by the anchoring parameter ξ is increased, the interfacial tension decreases and the bending rigidity first increases in ξ<ξ_{m}, and it then decreases in ξ_{m}<ξ. We explain these results by constructing a continuum field model based on the two order parameters: directional order of LC and the membrane shape. These order parameters are mutually interacting through the anchoring effect, the fluctuation coupling between the LC and the membrane, and the effect of the nematic layer.

Using a simple molecular model based on the Lennard–Jones potential, we systematically study the elastic properties of liquid–liquid interfaces containing surfactant molecules by means of extensive and large-scale molecular dynamics simulations. The main elastic constants of the interface, corresponding to the interfacial tension and the mean bending modulus are determined from the analyses of the long-wavelength behavior of the structure factor of the capillary waves. We found that the interfacial tension decreases with increasing surfactant interfacial coverage and/or surfactant chain length. However, we found that the corresponding change in the bending rigidity is nonmonotonic. Specifically, we found that the bending rigidity decreases with increasing surfactant interfacial coverage for small surfactant interface coverages, but then it increases as the surfactant interface coverage is further increased. Using a Gaussian theory on an interfacial Ginzburg–Landau model of surfactants, we find that the initial decrease of the bending rigidity is attributed to coupling between fluctuations of the surfactant orientation field to those in the interfacial height.

Effects of surface tension and Steigmann–Ogden surface elasticity on Hertzian contact properties