Anisotropic thermophoresis

Polymer Thermophoresis by Mesoscale Simulations

We employ mesoscopic simulations to study the thermophoretic motion of polymers in a solvent via multiparticle collision dynamics (MPCD). As the usual solvent-monomer collision rules employed in MPCD involving polymers fail to cause thermophoresis, we extend the technique by introducing explicit solvent-monomer interactions, while the solvent molecules remain ideal with respect to one another. We find that with purely repulsive polymer-solvent interaction, the polymer exhibits thermophilic behavior, whereas to display thermophobic behavior, the polymer-solvent potential requires the presence of attractions between solvent particles and monomers, in accordance with previous experimental findings. In addition, we observe that the thermophoretic mobility is independent of polymer length in the observed regime, again in agreement with experiments. Finally, we investigate the thermophoretic behavior of block copolymers, demonstrating that the thermophoretic mobility can be obtained by linear interpolation, weighted by the relative lengths of the two blocks.

Thermal conductivity effect on thermophoresis of charged spheroidal colloids in aqueous media

Thermophoresis of spheroidal colloids in aqueous media under the thermal conductivity effect is analyzed. The thermophoretic velocity and the thermodiffusion coefficient of spheroidal colloids have been formulated for extremely thin electric double layer (EDL) cases. Furthermore, a numerical thermophoretic model is built for arbitrary EDL thickness cases. The parametric studies show that the thermal conductivity mismatch of particle and liquid gives rise to a nonlinear temperature region around the spheroid, with the thickness close to the minor semiaxis. When the EDL region is thin relative to such nonlinear temperature region, the thermal conductivity effect on the thermophoresis of spheroidal colloids is significant, which strongly depends on the ratio of the minor semiaxis to the EDL thickness, the thermal conductivity ratio of particle to liquid, and the particle aspect ratio. Finally, to estimate the thermodiffusion coefficient of spheroidal colloids with arbitrary thermal conductivity, electrolyte concentration, and particle shape, the average dimensionless axial temperature gradient on the spheroidal equator plane in the EDL region is proposed.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

Analytical analysis of anisotropic thermophoresis of a charged spheroidal colloid in aqueous media for extremely thin EDL cases

Thermophoresis of charged spheroids has been widely applied in biology and medical science. In this work, we report an analysis of the anisotropic thermophoresis of diluted spheroidal colloids in aqueous media for extremely thin EDL cases. Under the boundary layer approximation, we formulate the thermophoretic velocity, the thermophoretic force, and the thermodiffusion coefficient of a randomly dispersed spheroid. The parametric studies show that under the aforementioned conditions, the thermophoresis is anisotropic and its thermodiffusion coefficient should be considered as a vector, D_T . The thermodiffusion coefficient values and directions of D_T are strongly related to the aspect ratio and the angle θ between the externally applied temperature gradient and the particle's axis of revolution: The increasing aspect ratio enlarges the thermodiffusion coefficient value D_T of prolate (oblate) spheroids to a constant value when θ < 60° (θ > 45°), and it reduces D_T of prolate (oblate) spheroids to a constant value when θ > 60° (θ < 45°). The thermodiffusion coefficient direction of both prolate and oblate spheroids deviates slightly from -∇T_∞ for a small aspect ratio, and such deviation becomes serious for a large aspect ratio.

Collective behavior of thermophoretic dimeric active colloids in three-dimensional bulk

Colloids driven by phoresis constitute one of the main avenues for the design of synthetic microswimmers. For these swimmers, the specific form of the phoretic and hydrodynamic interactions dramatically influences their dynamics. Explicit solvent simulations allow the investigation of the different behaviors of dimeric Janus active colloids. The phoretic character is modified from thermophilic to thermophobic, and this, together with the relative size of the beads, strongly influences the resulting solvent velocity fields. Hydrodynamic flows can change from puller-type to pusher-type, although the actual flows significantly differ from these standard flows. Such hydrodynamic interactions combined with phoretic interactions between dimers result in several interesting phenomena in three-dimensional bulk conditions. Thermophilic dimeric swimmers are attracted to each other and form large and stable aggregates. Repulsive phoretic interactions among thermophobic dimeric swimmers hinder such clustering and lead, together with long- and short-ranged attractive hydrodynamic interactions, to short-lived, aligned swarming structures.

A dissipative particle dynamics model for studying dynamic phenomena in colloidal rod suspensions

A dissipative particle dynamics (DPD) model is developed and demonstrated for studying dynamics in colloidal rod suspensions. The solvent is modeled as conventional DPD particles, while individual rods are represented by a rigid linear chain consisting of overlapping solid spheres, which interact with solvent particles through a hard repulsive potential. The boundary condition on the rod surface is controlled using a surface friction between the solid spheres and the solvent particles. In this work, this model is employed to study the diffusion of a single colloid in the DPD solvent and compared with theoretical predictions. Both the translational and rotational diffusion coefficients obtained at a proper surface friction show good agreement with calculations based on the rod size defined by the hard repulsive potential. In addition, the system-size dependence of the diffusion coefficients shows that the Navier-Stokes hydrodynamic interactions are correctly included in this DPD model. Comparing our results with experimental measurements of the diffusion coefficients of gold nanorods, we discuss the ability of the model to correctly describe dynamics in real nanorod suspensions. Our results provide a clear reference point from which the model could be extended to enable the study of colloid dynamics in more complex situations or for other types of particles.

Numerical Analysis of Thermophoresis of a Charged Spheroidal Colloid in Aqueous Media

Thermophoresis of charged colloids in aqueous media has wide applications in biology. Most existing studies of thermophoresis focused on spherical particles, but biological compounds are usually non-spherical. The present paper reports a numerical analysis of the thermophoresis of a charged spheroidal colloid in aqueous media. The model accounts for the strongly coupled temperature field, the flow field, the electric potential field, and the ion concentration field. Numerical simulations revealed that prolate spheroids move faster than spherical particles, and oblate spheroids move slower than spherical particles. For the arbitrary electric double layer (EDL) thickness, the thermodiffusion coefficient of prolate (oblate) spheroids increases (decreases) with the increasing particle’s dimension ratio between the major and minor semiaxes. For the extremely thin EDL case, the hydrodynamic effect is significant, and the thermodiffusion coefficient for prolate (oblate) spheroids converges to a fixed value with the increasing particle’s dimension ratio. For the extremely thick EDL case, the particle curvature’s effect also becomes important, and the increasing (decreasing) rate of thermodiffusion coefficient for prolate (oblate) spheroids is reduced slightly.

Forced Crowding of Colloids by Thermophoresis and Convection in a Custom Liquid Clusius-Dickel Microdevice

We report a study demonstrating that simultaneous induction of a steady-state convection current and temperature gradient in a confined geometry can be an effective way to force crowding of dissolved particulates. To investigate this thermogravitationally driven concentration of particles in situ, we developed a microdevice capable of sustaining controlled transverse temperature gradients within a 5 cm long, 0.1 mm inner diameter capillary that allowed visualization of particle movement with standard optical microscopy. Experiments were conducted on two material systems representative of nanoscale small molecules and microscale particles. With the small molecules (aromatic dyes, 530-790 g/mol, 1-1.5 nm), thermophoretic and gravitational effects in the microdevice resulted in an asymmetrical 2× concentration change along the capillary height over 3 days. In contrast, the concentration change under similar conditions for 40-micron diameter latex colloids is 50-fold in 30 min. This dramatic difference in separation times is consistent with simulations and models of thermophoresis where the thermophoretic effect scales with particle size. Induced crowding of particulates leads to formation of accumulation and depletion zones at the bottom and top of the capillary, respectively. Both the concentration of dye molecules over time in the depletion zone and the spatial distribution of colloids over the entire capillary length were found to be good fits to simple first-order exponential decay functions. These results suggest potential applications of thermogravitational separation in developing new functional materials via thermophoretic and convective effects.

A review of shaped colloidal particles in fluids: anisotropy and chirality

This review treats asymmetric colloidal particles moving through their host fluid under the action of some form of propulsion. The propulsion can come from an external body force or from external shear flow. It may also come from externally-induced stresses at the surface, arising from imposed chemical, thermal or electrical gradients. The resulting motion arises jointly from the driven particle and the displaced fluid. If the objects are asymmetric, every aspect of their motion and interaction depends on the orientation of the objects. This orientation in turn changes in response to the driving. The objects' shape can thus lead to a range of emergent anisotropic and chiral motion not possible with isotropic spherical particles. We first consider what aspects of a body's asymmetry can affect its drift through a fluid, especially chiral motion. We next discuss driving by injecting external force or torque into the particles. Then we consider driving without injecting force or torque. This includes driving by shear flow and driving by surface stresses, such as electrophoresis. We consider how time-dependent driving can induce collective orientational order and coherent motion. We show how a given particle shape can be represented using an assembly of point forces called a Stokeslet object. We next consider the interactions between anisotropic propelled particles, the symmetries governing the interactions, and the possibility of bound pairs of particles. Finally we show how the collective hydrodynamics of a suspension can be qualitatively altered by the particles' shapes. The asymmetric responses discussed here are broadly relevant also for swimming propulsion of active micron-scale objects such as microorganisms.

Dissipative particle dynamics with energy conservation: Isoenergetic integration and transport properties

Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle dynamics with energy conservation (DPDE), which has been used for various fluid systems with non-uniform temperature distributions. We propose an easily parallelizable modification of the velocity-Verlet algorithm based on local energy redistribution for each DPDE particle such that the total energy in a simulated system is conserved up to machine precision. Furthermore, transport properties of a DPDE fluid are analyzed in detail. In particular, an analytical approximation for the thermal conductivity coefficient is derived, which allows its a priori estimation for a given parameter set. Finally, we provide approximate expressions for the dimensionless Prandtl and Schmidt numbers, which characterize fluid transport properties and can be adjusted independently by a proper selection of model parameters. In conclusion, our results strengthen the DPDE method as a very robust approach for the investigation of mesoscopic systems with temperature inhomogeneities.

Growth of Colloidal Nanoplate Liquid Crystals Using Temperature Gradients

Controlling colloidal self-assemblies using external forces is essential to develop modern electro-optical and biomedical devices. Importantly, shape anisotropic colloids can provide optical properties such as birefringence. Here we demonstrate that external temperature gradients can be effective in controlling nematic liquid crystalline (LC) order in suspensions of plate-like colloids also known as nanoplates. Nanoplates, in an isotropic suspension, wherein their orientations are random, could be effectively moved using a temperature gradient environment causing a phase transition to LC nematic phase. Such controllably formed nematic phase featured large nematic monodomains and enabled topologically more stable structures that were evident from the absence of hedgehog-type defects which are typically found in nematics formed spontaneously via nucleation and growth mechanism in a sufficiently high concentration suspension of nanoplates. Due to their high surface area-to-volume ratio and excellent thermophoretic properties, nanoplates can prove to be ideal candidates for transport of biomolecules through temperature varying environments.

Thermoosomosis in microfluidic devices containing a temperature gradient normal to the channel walls

We analyze a microfluidic pump from the literature that utilizes a flat channel with boundary walls at different temperatures and tilted elongated pillars within in order to construct an adequate theory for designing devices in which the temperature gradient between channel walls is transformed into a longitudinal temperature gradient along the channel length. The action of the device is based on thermoosmosis in the secondary longitudinal temperature gradient associated with the specific geometry of the device, which can be described using physicochemical hydrodynamics without invoking the concept of thermophoretic force. We also describe a rotating drive device based on the same principle and design.

Universal optimal geometry of minimal phoretic pumps

Unlike pressure-driven flows, surface-mediated phoretic flows provide efficient means to drive fluid motion on very small scales. Colloidal particles covered with chemically-active patches with nonzero phoretic mobility (e.g. Janus particles) swim using self-generated gradients, and similar physics can be exploited to create phoretic pumps. Here we analyse in detail the design principles of phoretic pumps and show that for a minimal phoretic pump, consisting of 3 distinct chemical patches, the optimal arrangement of the patches maximizing the flow rate is universal and independent of chemistry.

Thermal orientation and thermophoresis of anisotropic colloids: The role of the internal composition

The drift motion experienced by colloids immersed in a fluid with an intrinsic temperature gradient is referred to as thermophoresis. An anisotropic mass distribution inside colloidal particles imparts a net orientation with respect to the applied thermal field, and in turn alters the thermophoretic response of the colloids. This rectification of the rotational Brownian motion is called thermal orientation. To explore the sensitivity of the thermal orientation effect with the internal composition of colloids, we investigate the thermophoretic response of rod-like colloids in the dilute regime, targeting different internal mass distributions. We derive phenomenological equations to model the dependence of the Soret coefficient with degree of mass anisotropy and test these equations using non-equilibrium molecular dynamics simulations. Using both theory and simulation, we show that the average orientation and the Soret coefficients of the colloids can depend significantly on the internal mass distribution. This observation suggests an approach to identify internal colloidal compositions using thermal gradients as sensing probes.

Configurational contribution to the Soret effect of a protein ligand system : An investigation with density-of-states simulations

Many of the biological functions of proteins are closely associated with their ability to bind ligands and change conformations in response to changing conditions. Since binding state and conformation of a protein affect its response to a temperature gradient, they may be probed with thermophoresis. In recent years, thermophoretic techniques to investigate biomolecular interactions, quantify ligand binding, and probe conformational changes have become established. To develop a better understanding of the mechanisms underlying the thermophoretic behavior of proteins and ligands, we employ a simple, off-lattice model for a protein and ligand in explicit solvent. To investigate the partitioning of the particles in a temperature gradient, we perform Wang-Landau-type simulations in a divided simulation box and construct the density of states over a two-dimensional state space. This method gives us access to the entropy and energy of the divided system and allows us to estimate the configurational contribution to the Soret coefficient. In this work, we focus on dilute solutions of hydrophobic proteins and investigate the effect of ligand binding on their thermophoretic behavior. We find that our simple model captures important aspects of protein-ligand interactions and allows us to relate the binding energy to the change in Soret coefficient upon ligand binding.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λ_DH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol^-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, D_T, of the bare virus increases strongly with the Debye length, whereas D_T of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of D_T as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of D_T of PEG and the offset of the bare fd-virus. At high λ_DH, corresponding to the low ionic strength, the S_T values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λ_DH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Theoretical description of the thermomolecular orientation of anisotropic colloids

We describe theoretically the orientation of anisotropic colloids under a thermal field.

Thermo-orientation in fluids of arbitrarily shaped particles

Recent nonequilibrium Molecular Dynamics (NEMD) simulations revealed preferential orientation, induced by a temperature gradient, in fluids of uncharged dumbbell-like particles. The magnitude of this phenomenon, called thermo-orientation, was found to be linear in the applied temperature gradient and to increase with the difference in shape or mass between the two beads of the particles. The underlying mechanism and the microscopic determinants of the phenomenon are not obvious. Here, after examination of the general symmetry requirements for thermo-orientation, we have extended the NEMD simulations to uncharged particles of various shapes and mass distribution, including chiral cases. The numerical results are rationalized by a microscopic model, based on the assumption of local equilibrium. This allows us to correlate the thermo-orientation response of arbitrarily shaped particles to quantities that characterize their shape and mass distribution.

Thermophoretic torque in colloidal particles with mass asymmetry

We investigate the response of anisotropic colloids suspended in a fluid under a thermal field. Using nonequilibrium molecular dynamics computer simulations and nonequilibrium thermodynamics theory, we show that an anisotropic mass distribution inside the colloid rectifies the rotational Brownian motion and the colloids experience transient torques that orient the colloid along the direction of the thermal field. This physical effect gives rise to distinctive changes in the dependence of the Soret coefficient with colloid mass, which features a maximum, unlike the monotonic increase of the thermophoretic force with mass observed in homogeneous colloids.