Influence Of Hydrodynamic Interactions Research Articles

Influence of hydrodynamic interactions among multiple bubbles on convective heat transfer in nucleate boiling

To clear the effects of the hydrodynamic interactions among neighboring vapor bubbles on the saturated pool boiling heat transfer, artificial nucleation sites with several cavity arrangements were manufactured on the substrate surface and measured liquid temperatures near heated substrate by a miniature thermocouple probe with 10 kHz. The surface temperature of heated substrate was measured by an infrared camera with 1 kHz and bubble dynamics were simultaneously visualized by a high-speed video camera with 5 kHz and 10 kHz, respectively. The liquid temperature fluctuations, measured with micro thermocouple 100 μm and 10 μm above the substrate surface, were compared among each other and with the transient temperature fields obtained through IR measurements. Results showed that the hydrodynamic interaction among neighboring bubbles causes the liquid convection, that was only detected 100 µm above the boiling surface. Generally, the degree of liquid temperature fluctuations at 10 μm height and different arrangements of nucleation sites was under 1 K. Here the superheated sublayer in the vicinity of the boiling surface was generally not affected by the convection. Only when the coalescence from two neighboring nucleation sites occurred and the liquid-vapor interface nearly reached the substrate, a steep temperature drop over 2 K was detected. It was concluded that the viscous sublayer stably exists during boiling of water in lower heat flux conditions. To enhance the convective heat transfer in nucleate boiling, coalesced bubble needs to peel off the viscous sublayer during its deformation. Based on the measurements in this study, this peel-off effect only happens when the coalescence point is less than 1 mm above the heated surface.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles.

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.

The stretching force on a tethered polymer in pressure-driven flow.

We use mesoscopic lattice-Boltzmann/molecular dynamics simulations to study the stretching behavior of a single tethered polymer in micro- and nanochannels. In particular, we are interested in the connection between fluid flow properties and the force on the polymer chain. An analytical expression for the stretching force is proposed, which linearly depends on the number of monomers and the boundary shear rate. In agreement with theory, the numerical findings reveal that the influence of hydrodynamic interactions can be ignored, which is also supported by results of additional Langevin dynamics simulations. Our simulation data coincide with the analytical expression for the fractional extension of the chain and further indicate that even weak Poiseuille flow profiles induce a strong alignment of the chain along the channel walls. The numerical results are in good agreement with experimental data obtained by microfluidic stretching of tethered λ-DNA.

Dynamics of Branched Polymers in Random Layered Flows with Intramolecular Hydrodynamic Coupling: Star and Dendrimer

The authors develop a theoretical formalism to incorporate the effect of intramolecular hydrodynamic interactions (HIs) on the dynamics of flexible branched polymer in the presence of random layered flows. The influence of HIs on the anomalous diffusive behavior of branched polymers is illustrated through the preaveraged Oseen tensor approach. Although the formalism is valid for polymer structures with arbitrary topology, particular attention is paid here to the study of stars and dendrimers. The macromolecular property that is evaluated is the average square displacement (ASD) of drift center of the polymer. Qualitatively, our analysis highlights two anomalous power‐law regimes, viz. subdiffusive (intermediate‐time polymer stretching and flow induced diffusion) and superdiffusive (long‐time flow induced diffusion). The time dependence of the ASD in the presence of HIs within the preaveraging approximation reveals the anomalous long‐time dynamics which is governed by scaling behavior, t2 − α/2. The introduction of HIs in random flows speeds up the dynamics resulting in the shorter crossover time (from subdiffusive to superdiffusive regime) with enhanced magnitude of ASD compared to the free‐draining limit. image

Reactive Mass Transfer of Single NO Bubbles and Bubble Bouncing in Aqueous Ferric Solutions – A Feasibility Study

Reactive bubble columns are widely used in the chemical, petrochemical, biochemical and metal industries. While the reactive mass transfer around a single spherical shaped bubble is quite well described in literature, the influence of hydrodynamic interactions, such as bubble bouncing or coalescence on mass transfer – with and without chemical reaction – is not well understood. As to this, high resolution simulations and sophisticated experimental analysis based on high-speed camera images and local color changes gives a new firm basis. In this work, a new system is presented, based on Nitric Oxide (NO) gas absorbed in a FeII-solution. The reaction rate can be adjusted by the addition of ligands and the resulting local color change is detected. The impact of the colliding bubbles leads to a deformation of the bubble shapes and creates a fast movement of the bubble interfaces, which, finally, leads to an increased mass transfer. The results of five tested ligands reveal the high potential of the reactive FeII(NO) system to investigate basic phenomena affecting yield and selectivity of mixing-sensitive chemical reactions.

Detention Times of Microswimmers Close to Surfaces: Influence of Hydrodynamic Interactions and Noise.

After colliding with a surface, microswimmers reside there during the detention time. They accumulate and may form complex structures such as biofilms. We introduce a general framework to calculate the distribution of detention times using the method of first-passage times and study how rotational noise and hydrodynamic interactions influence the escape from a surface. We compare generic swimmer models to the simple active Brownian particle. While the respective detention times of source dipoles are smaller, the ones of pullers are larger by up to several orders of magnitude, and pushers show both trends. We apply our results to the more realistic squirmer model, for which we use lubrication theory, and validate them by simulations with multiparticle collision dynamics.

The detrimental effect of hydrodynamic interactions on the process of Brownian flocculation in shear flow

AbstractThe problem of Brownian flocculation of spherical particles in strong shearing flow without hydrodynamic interactions is studied in detail using the singular perturbation method. All other types of interparticle interactions, such as van der Waals or Lennard-Jones forces, are also ignored. In the limit of strong external flow, the strength of which is measured by the Péclet number ($Pe\gg 1$), a complicated boundary layer structure for the pair probability density function ($P_{2}$) is identified and the complete stationary spatial distribution of $P_{2}(\boldsymbol {x})$ in the domain is found. The results, in particular the total mass flux in the accumulation process, are compared qualitatively and quantitatively with the case where the spheres interact hydrodynamically and it is demonstrated that the hydrodynamic interactions tend to decrease the rate of flocculation. An explicit simple formula for the flocculation rate for a general form of hydrodynamic interactions is provided. The limit of small Péclet number is also discussed to confirm the conclusion on the detrimental influence of hydrodynamic interactions on the rate of Brownian flocculation in shearing flow.

Cosmology in a petri dish? Simulation of collective of colloids at fluid interfaces

Interfacially trapped, micrometer-sized colloidal particles interact via ranged capillary attraction which is analogous to two-dimensional screened Newtonian gravity with the capillary length λ as the tuneable screening length. Using Brownian namics simulations and density functional theory, we study the dynamics of an initially prepared distribution of colloids, either a random homogeneous distribution, or a finitely- sized patch of colloids. Whereas the limit λ → ∞ corresponds to the global collapse self-gravitating fluid, for smaller λ the dynamics crosses over to spinodal decomposition showing a coarsening of regions of enhanced density which emerge from initial fluctuations. For the finite patch of colloids and intermediate λ we predict theoretically and serve in simulations a ringlike density peak at the outer rim of the disclike patch, moving as an inbound shock wave. Experimental realizations of this crossover scenario appear be well possible for colloids trapped at water interfaces and having a radius of around micrometer. Finally, the influence of hydrodynamic interactions on this capillary collapse will be discussed briefly.

Single-file diffusion in periodic energy landscapes: The role of hydrodynamic interactions

We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.

The influence of hydrodynamic interactions on protein dynamics in confined and crowded spaces—assessment in simple models

We consider several systems that are confined within a softly repulsive sphere. The first one is a model protein, crambin, which is described by a structure-based coarse grained model. We demonstrate that the folding process is accelerated by the hydrodynamic interactions (HI) in a way that depends on the radius of the sphere. The tighter the encompassing sphere, the smaller the effect, independent of the nature of the starting conformations. The second system is a protein surrounded by protein-like softly repulsive spheres that make the confined space crowded. In this case, the HI shorten the folding times in a way which depends on the degree of crowdedness only weakly. The third system is a collection of spheres that are meant to represent molecules. We show that confinement increases association times. We also observe that the HI either facilitate or obstruct association of two spheres depending on the crowding conditions. The dependence of the association time on crowdedness in the confining sphere is qualitatively distinct from that derived by Wieczorek and Zielenkiewicz for a cube with the periodic boundary conditions.

Collapse Dynamics of Copolymers in a Poor Solvent: Influence of Hydrodynamic Interactions and Chain Sequence

We investigate the dynamics of the collapse of a single copolymer chain, when the solvent quality is suddenly quenched from good to poor. We employ Brownian dynamics simulations of a bead-spring chain model and incorporate fluctuating hydrodynamic interactions via the Rotne-Prager-Yamakawa tensor. Various copolymer architectures are studied within the framework of a two-letter HP model, where monomers of type H (hydrophobic) attract each other, while all interactions involving P (polar or hydrophilic) monomers are purely repulsive. The hydrodynamic interactions are found to assist the collapse. Furthermore, the chain sequence has a strong influence on the kinetics and on the compactness and energy of the final state. The dynamics is typically characterised by initial rapid cluster formation, followed by coalescence and final rearrangement to form the compact globule. The coalescence stage takes most of the collapse time, and its duration is particularly sensitive to the details of the architecture. Long blocks of type P are identified as the main bottlenecks to find the globular state rapidly.

Structural instability in the sedimentation of particulate suspensions through viscoelastic fluids

A theory is developed to describe a structural instability that has been observed during the sedimentation of particulate suspensions through viscoelastic fluids. The theory is based on the assumption that the influence of hydrodynamic interactions in viscoelastic fluids, which tend to cause particles to aggregate, is in competition with hydrodynamic dispersion, which acts to maintain a homogeneous microstructure. In keeping with the experimental observations, it predicts that the suspension structure will stratify into vertical columns when a dimensionless stability parameter exceeds a critical value. The column-to-column separation, measured in particle radii, is predicted to be proportional to the square root of the ratio of the dimensionless dispersion coefficient to the product of the particle volume fraction and the Deborah number. The time for the formation of the columns is predicted to scale with the inverse of the average volume fraction. These predictions are in agreement with experimental data reported in the literature.

Influence of hydrodynamic interactions on lane formation in oppositely charged driven colloids

The influence of hydrodynamic interactions on lane formation of oppositely charged driven colloidal suspensions is investigated using Brownian dynamics computer simulations performed on the Rotne-Prager level of the mobility tensor. Two cases are considered, namely sedimentation and electrophoresis. In the latter case the Oseen contribution to the mobility tensor is screened due to the opposite motion of counterions. The simulation results are compared to that resulting from simple Brownian dynamics where hydrodynamic interactions are neglected. For sedimentation, we find that hydrodynamic interactions strongly disfavor laning. In the steady state of lanes, a macroscopic phase separation of lanes is observed. This is in marked contrast to the simple Brownian case where a finite size of lanes was obtained in the steady state. For strong Coulomb interactions between the colloidal particles a lateral square lattice of oppositely driven lanes is stable similar to the simple Brownian dynamics. In an electric field, on the other hand, the behavior is found in qualitative and quantitative accordance with the case of neglected hydrodynamics.

Influence of hydrodynamic interactions on mechanical unfolding of proteins

We incorporate hydrodynamic interactions in a structure-based model of ubiquitin anddemonstrate that the hydrodynamic coupling may reduce the peak force when stretchingthe protein at constant speed, especially at larger speeds. Hydrodynamic interactions arealso shown to facilitate unfolding at constant force and inhibit stretching by fluid flows.

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations.

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.

Brownian dynamics simulations of the effects of hydrodynamic interactions on the polymer viscoelastic behavior

Brownian dynamics simulation is used to investigate the viscoelastic response of the Gaussian chain to a step shear deformation in both the linear and non-linear regions under the influence of hydrodynamic interactions. Both the preaveraged Oseen tensor and the Rotne–Prager tensor are used in the study. In the former case, the simulation results are shown to be in agreement with the expected results calculated using the eigenvalues of the normal modes of motion obtained numerically. It is shown that an initial state with zero second normal-stress difference is generated by the step shear deformation. The subsequent rise of the second normal-stress difference as revealed by the simulation is shown mainly arising from the coupling of the recoil of the stretched bond in the direction of deformation and the anisotropy in the hydrodynamic interaction created by the step deformation.

Tracer-diffusion in binary colloidal hard-sphere suspensions

We calculate the short-time translational and rotational self-diffusion coefficients of mixtures of colloidal hard spheres. The influence of hydrodynamic interactions is accounted for by a series expansion of the two-body mobility tensors, and by considering the leading hydrodynamic three-body term. Explicit results are presented for the rotational–translational diffusion coefficients, Ds,Tr and Ds,Tt, of a dilute tracer component in a concentrated host dispersion of hard spheres. These coefficients are shown to depend strongly on the host volume fraction, φ, and on the size ratio, λ, of tracer and host particles. For large λ, the tracer diffusion coefficients are related to the viscosity of the host dispersion by effective Stokes–Einstein relations.

Influence of hydrodynamic interactions between particles on the turbulent flow in a suspension

A model based on the theory of Felderhof and Ooms [Phys. Fluids A 1 (1989) 1091] is used to evaluate the effect of hydrodynamic interactions between particles in turbulent two-phase flows. The particles are assumed to be point-particles, obeying Stokes' drag law. The flow of the suspending fluid phase is assumed to be (stochastic) stationary, homogeneous, isotropic turbulence. To simplify the calculations, only two-particle hydrodynamic interactions are taken into account. The value of the reduction function J, which is a measure of the hydrodynamic interactions, is evaluated as a function of the dimensionless wave number and frequency for a range of values of the density ratio between fluid and particles. Only for relatively heavy particles, hydrodynamic interactions affect the reduction function J and the corresponding spectral transfer functions. However, it was found that the effect of the interactions between point-particles could be neglected in turbulent flows, since very little energy is present at the frequencies where the interactions took place.

Polyelectrolyte/post collisions during electrophoresis: Influence of hydrodynamic interactions

We consider the interaction of an homogeneous polyelectrolyte with an obstacle during electrophoretic drift. We explicitly take into account the hydrodynamic interactions generated by this mechanical trapping, and we evaluate their influence on the unhooking process. Important qualitative effects are pointed out in low and moderate field regimes. However, numerical simulations indicate that, in strong field, the existing simpler local force models, which neglect these hydrodynamic interactions, are quantitatively acceptable.

Tracer-diffusion in colloidal mixtures: A mode-coupling scheme with hydrodynamic interactions

In this work, we develop a general theoretical scheme to study tracer-diffusion in mixtures of interacting colloidal particles where the influence of solvent-mediated hydrodynamic interactions is also considered. Based on the many-body Smoluchowski diffusion equation, we derive in a first step an exact microscopic expression of the irreducible memory function (self-friction function) associated with the self-intermediate scattering function and with the mean squared displacement of a tagged particle. By applying a mode-coupling scheme (MCS) to the irreducible memory function, we obtain explicit expressions for the tracer-diffusion quantities in terms of partial static structure factors and hydrodynamic functions. The influence of hydrodynamic interactions (HI) is accounted for using a far-field expansion of the two-body hydrodynamic diffusivity tensors. For charge-stabilized colloids, this is a good approximation due to strong electrostatic repulsion between the particles. Various applications are discussed in order to illustrate the versatility of our mode-coupling scheme.