Computer simulation on the collision-sticking dynamics of two colloidal particles in an optical trap

Collisions of a particle pair induced by optical tweezers have been employed to study colloidal stability. In order to deepen insights regarding the collision-sticking dynamics of a particle pair in the optical trap that were observed in experimental approaches at the particle level, the authors carry out a Brownian dynamics simulation. In the simulation, various contributing factors, including the Derjaguin-Landau-Verwey-Overbeek interaction of particles, hydrodynamic interactions, optical trapping forces on the two particles, and the Brownian motion, were all taken into account. The simulation reproduces the tendencies of the accumulated sticking probability during the trapping duration for the trapped particle pair described in our previous study and provides an explanation for why the two entangled particles in the trap experience two different statuses.     

Propulsion and trapping of microparticles by active cilia arrays

We model the transport of a microscopic particle via a regular array of beating elastic cilia, whose tips experience an adhesive interaction with the particle's surface. At optimal adhesion strength, the average particle velocity is maximized. Using simulations spanning a range of cilia stiffness and cilia-particle adhesion strength, we explore the parameter space over which the particle can be "released", "propelled", or "trapped" by the cilia. We use a lower-order model to predict parameters for which the cilia are able to "propel" the particle. This is the first study that shows how both stiffness and adhesion strength are crucial for manipulation of particles by active cilia arrays. These results can facilitate the design of synthetic cilia that integrate adhesive and hydrodynamic interactions to selectively repel or trap particulates. Surfaces that are effective at repelling particulates are valuable for antifouling applications, while surfaces that can trap and, thus, remove particulates from the solution are useful for efficient filtration systems.     

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.     

Effect of Rotary Inertia on the Orientational Behavior of Dilute Brownian and Non-Brownian Fiber Suspensions

The orientational behavior of a dilute suspension of slender Brownian and non-Brownian fibers with rotary inertia in simple shear and turbulent channel flows is numerically investigated. The translational inertia of fibers is neglected. The equations describing the evolution of fibers orientation are integrated along the Lagrangian paths of the fluid elements. The fully developed turbulent channel flow at Re _τ = 180 is provided by a direct numerical simulation (DNS). The coupling between the flow field and the fiber dynamics is one way. The Brownian motion is modeled by a stochastic Wiener process. The results are compared with those of inertia-free particles. In simple shear flow, the inertial non-Brownian fibers align slower than the inertia-free fibers to the shear direction while they tend to the same steady state orientation. For Brownian fibers, the steady state orientation of inertial and inertia-free fibers differ. In turbulent channel flow, the second moment of the orientation distribution function shows an oscillatory behavior at high values of inertia for non-Brownian fibers while the oscillations disappear at lower inertia. For Brownian fibers, the oscillations are weaker due to the damping effect of the Brownian diffusivity.     

Importance of particle tracking and calculating the mean-squared displacement in distinguishing nanopropulsion from other processes

In this paper we show that processes such as Brownian motion, convection, sedimentation, and bacterial contamination can cause small particles to move through liquids in a fashion which may be mistaken as nanopropulsion. It is shown that particle tracking and subsequent statistical analysis is essential to ascertain if small particles actually propel themselves, or if they are propelled by another process. Specifically we find that it is necessary to calculate the mean-squared displacement of particles at both short and long time intervals, to show that the direction of propulsion changes coincident with rotation of the particle by Brownian motion, as this allows nanopropulsion to be differentiated from Brownian motion, convection and sedimentation. We also find that bacteria can attach themselves to particles and cause them to be propelled. This leads to motion which appears very similar to nanopropulsion and cannot be differentiated using particle tracking and therefore find that carefully designed control experiments must be performed. Finally, we suggest an experimental protocol which can be used to investigate the motion of small objects and prove if they move due to nanopropulsion.     

Elastic coefficient of a single polymer chain by using Brownian dynamics analysis

The elastic coefficient of a single polystyrene chain has been experimentally evaluated by using Brownian dynamics analysis. The Brownian motion of the chain is probed using a particle trapped by optical tweezers with a negligibly small spring constant. The displacement of the particle due to Brownian motion is measured by an interferometer assembled using the same laser beam as the optical tweezers. Two methods are employed for Brownian dynamics analysis: (1) the analysis of the time course of the displacement of the particle and (2) the fitting of the power spectrum of Brownian motion with a Lorentzian. The elastic constant of a polystyrene chain in dichloromethane at 21 degrees C is estimated to be 6.4 x 10(-6) and 1.1 x 10(-5) N/m when methods (1) and (2) are employed, respectively. The elastic constant obtained by approximating the polystyrene chain to a freely jointed chain is in agreement with the experimentally evaluated elastic constant.     

Diffusing-wave spectroscopy and interferometry

Diffusing-wave spectroscopy and interferometry, the extensions of dynamic light scattering to materials which exhibit a very high degree of multiple scattering, have been used to measure the early-time, short length scale motion of Brownian particles. The transition from “ballistic” to “diffusive” motion is observed. In very dilute samples, this transition is described very well by theories which explicitly account for the time-dependent hydrodynamic interaction between a Brownian particle and the surrounding fluid. For particle volume fractions exceeding a few per cent, the data deviate from the theory for dilute suspensions, but exhibit a remarkable scaling with the suspension viscosity.     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

A microfluidic-based hydrodynamic trap: design and implementation

We report an integrated microfluidic device for fine-scale manipulation and confinement of micro- and nanoscale particles in free-solution. Using this device, single particles are trapped in a stagnation point flow at the junction of two intersecting microchannels. The hydrodynamic trap is based on active flow control at a fluid stagnation point using an integrated on-chip valve in a monolithic PDMS-based microfluidic device. In this work, we characterize device design parameters enabling precise control of stagnation point position for efficient trap performance. The microfluidic-based hydrodynamic trap facilitates particle trapping using the sole action of fluid flow and provides a viable alternative to existing confinement and manipulation techniques based on electric, optical, magnetic or acoustic force fields. Overall, the hydrodynamic trap enables non-contact confinement of fluorescent and non-fluorescent particles for extended times and provides a new platform for fundamental studies in biology, biotechnology and materials science.     

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.     

Selectivity principle of the ligand escape process from a two-gate tunnel in myoglobin: molecular dynamics simulation

We proposed a selectivity principle for the ligand escape process from two fluctuating bottlenecks in a cavity with a multigate inside a myoglobin pocket. Our previous analytical theory proposed a fluctuating bottleneck model for a Brownian particle passing through two gates on a cavity surface of an enzyme protein and has determined the escape rate in terms of the time-dependent gate function and the competition effect. It illustrated that with two (or more than two) gates on a cavity surface the gate modulation, which is controlled by protein fluctuation, dominates the ligand escape pathway. We have performed a molecular dynamics simulation to investigate the selectivity principle of the ligand escape process from two-gate tunnel in myoglobin. The simulation results confirm our theoretical conjecture. It indicates that the escape process is actually entropy driven, and the ligand escape pathway is chosen via the gate modulation. This suggests an interesting intrinsic property, that is, the oxymyoglobin tertiary structure is favorable to the departure of the ligand from one direction rather than through a biased random walk.     

Spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall

The spectrum of position fluctuations of a Brownian particle bound in a harmonic trap near a plane wall is calculated from an approximate result for the Fourier transform of the velocity autocorrelation function. Both a no-slip and a perfect slip boundary condition at the wall are considered. In both cases at low frequency the calculated spectrum differs markedly from recent experimental data. It is suggested that a partial slip boundary condition with a frequency-dependent slip coefficient may explain the experimental results.     

Measurement of long-range forces on a single yeast cell using a gradient optical trap and evanescent wave light scattering

The long-range equilibrium and viscous interaction forces between a single Candida albicans cell and a flat surface have been measured using a gradient optical trap as a force transducer and evanescent wave light scattering (EWLS) to determine the separation distance. In this technique the trapped cell is probed against the surface by moving the focal point of the optical trap, the equilibrium force is determined by the deflection of the most probable cell position from the trap center, and the viscous forces are determined from the relaxation time of the Brownian fluctuations of the cell in the trap. At low electrolyte concentrations (0.5 mM NaCl) where double layer repulsion was anticipated to be the dominant interaction, equilibrium force–distance profiles for yeast cells and similarly sized polystyrene microspheres on glass surfaces both showed good agreement with predictions of DLVO theory. Also, viscous drag profiles at larger separation distances where interaction forces were small agreed well with Stokes flow predictions. These results appear to validate the technique for use with spherical yeast cells and other bioparticles of similar size. This force measurement methodology therefore provides a complementary alternative to atomic force microscopy for direct force measurement with much greater sensitivity for studying interaction between yeast and surfaces.     

The van Hove distribution function for brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics

We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the "self?" component having only one particle, the "distinct" component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components. We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan-Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.     

Mobility matrix of a spherical particle translating and rotating in a viscous fluid confined in a spherical cell, and the rate of escape from the cell

The mobility matrix of a spherical particle moving in a spherical cavity, filled with a viscous incompressible fluid, and with no-slip boundary condition at the wall of the cavity, is evaluated from the Oseen tensor for the cavity by the method used by Lorentz for a particle near a planar wall. For the case that the particle is a rigid sphere with no-slip boundary condition the comparison with exact calculations shows that the approximation is quite accurate, provided the radius of the particle is small relative to that of the cavity, and provided the particle is not too close to the wall. The translational mobility is used to derive the diffusion tensor of a Brownian particle via an Einstein relation. The approximate result for the diffusion tensor is employed to estimate the rate of escape of a Brownian particle from a cavity with semipermeable wall.     

Quantum dynamics of a charged particle in a penning trap

With the help of the exact classical path representation of the time dependent propagator the dynamics of a charged particle in a Penning trap in the presence of an additional classical, time-dependent electric field is investigated. In this way the connection between quantum and classical dynamics is exhibited in a clear way. The possibility of localizing a particle in the ground state of a Penning trap with unit probability by a suitably chosen electric field is discussed.     

Dwell time of a Brownian molecule in a microdomain with traps and a small hole on the boundary

We calculate the mean time a Brownian particle spends in a domain with traps and the number of bonds it makes before escaping through a small hole in the boundary. This mean time, called the Dwell time, depends on the backward binding rate (with the trap, e.g., scaffolding molecules), the mean time to reach the trap (forward binding rate), and the size of the hole. We estimate the mean and variance of the number of bonds made prior to exit. In a biochemical context, a quantitative signal occurs when the mean number of bonds exceeds a certain threshold, which may initiate a cascade of chemical reactions that have physiological consequences. We apply the present results to obtain estimates of the mean time a Brownian receptor spends inside a synaptic domain, when it moves freely by lateral diffusion on the membrane of a neuron and interacts at a synapse with scaffolding molecules.     

Manipulating nanoparticles in solution with electrically contacted nanotubes using dielectrophoresis

Dielectrophoresis is an electronic analogue1,2 of optical tweezers3 based on the same physical principle: an ac electric field induces a dipole moment on an object in solution, which then experiences a force proportional to the gradient of the field intensity. For both types of tweezers, this force must compete with thermal Brownian4 motion to be effective, which becomes increasingly difficult as the particle size approaches the nanometer scale. Here we show that this restriction can be overcome by using the large electric field gradient in the vicinity of a carbon nanotube to electronically manipulate nanoparticles down to 2 nm in diameter.     

Transient diffusion in a tube with dead ends

A particle diffusing in a tube with dead ends, from time to time enters a dead end, spends some time in the dead end, and then comes back to the tube. As a result, the particle spends in the tube only a part of the entire observation time that leads to slowdown of its diffusion along the tube. We study the transient diffusion in a tube with periodic identical dead ends formed by cavities of volume V(cav) connected to the tube by cylindrical channels of length L and radius a, which is assumed to be much smaller than the tube radius R and the distance l between neighboring dead ends. Assuming that the particle initial position is uniformly distributed over the tube, we analyze the monotonic decrease of the particle diffusion coefficient D(t) from its initial value D(0)=D, which characterizes diffusion in the tube without dead ends, to its asymptotic long-time value D(infinity)=D(eff)相似文献   

A Protocol for the Estimation of Parameters in Process Models: Case Studies with Polymerization Scenarios

Summary: As our understanding of chemical processes increases, the complexity of the models developed to describe them also increases. In most cases the equations are nonlinear in the inputs and parameters, and must be solved numerically. At present in estimating parameters for large process models, there are two shortcomings in the existing knowledge about (multiresponse) parameter estimation. The first is, how effective is the present parameter estimation methodology when applied to large models, and the second is, can any advantage be gained from considering the parameter estimation problem as a whole. This paper will address these questions, by revisiting the various steps of a parameter estimation protocol. There is little discussion in the literature as to how all the steps for parameter estimation are related. In the development of this protocol all of the steps for parameter estimation will be revisited: parameter sensitivity analysis, statistical design of experiments, estimation of parameters and confidence regions. By considering all these steps as a whole the overall parameter estimation procedure can be more efficient and some pitfalls, such as local optima and incorrect confidence regions, may be dealt with in an appropriate manner. To illustrate the application of the protocol, two case studies related to polymerization models are presented. These case studies illustrate some of the problems that may be encountered in the parameter estimation process and how the proposed protocol can aid in overcoming them.

Plot of conversion versus time for the copolymerization of styrene/methyl methacrylate.