Hydrodynamic Interactions, colloidal

Adler, P.M. (1981). Interaction of unequal spheres I. Hydrodynamic interaction colloidal forces. J. Colloid Interface Set, 84, 461-473. 

There are several attractive features of such a mesoscopic description. Because the dynamics is simple, it is both easy and efficient to simulate. The equations of motion are easily written and the techniques of nonequilibriun statistical mechanics can be used to derive macroscopic laws and correlation function expressions for the transport properties. Accurate analytical expressions for the transport coefficient can be derived. The mesoscopic description can be combined with full molecular dynamics in order to describe the properties of solute species, such as polymers or colloids, in solution. Because all of the conservation laws are satisfied, hydrodynamic interactions, which play an important role in the dynamical properties of such systems, are automatically taken into account. 

Multiparticle collision dynamics can be combined with full molecular dynamics in order to describe the behavior of solute molecules in solution. Such hybrid MPC-MD schemes are especially useful for treating polymer and colloid dynamics since they incorporate hydrodynamic interactions. They are also useful for describing reactive systems where diffusive coupling among solute species is important. 

Most descriptions of the dynamics of molecular or particle motion in solution require a knowledge of the frictional properties of the system. This is especially true for polymer solutions, colloidal suspensions, molecular transport processes, and biomolecular conformational changes. Particle friction also plays an important role in the calculation of diffusion-influenced reaction rates, which will be discussed later. Solvent multiparticle collision dynamics, in conjunction with molecular dynamics of solute particles, provides a means to study such systems. In this section we show how the frictional properties and hydrodynamic interactions among solute or colloidal particles can be studied using hybrid MPC-MD schemes. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

J. T. Padding and A. A. Louis, Hydrodynamic interactions and Brownian forces in colloidal suspensions coarse-graining over time and length scales, Phys. Rev. E 74, 031402 (2006). 

In this group of disperse systems we will focus on particles, which could be solid, liquid or gaseous, dispersed in a liquid medium. The particle size may be a few nanometres up to a few micrometres. Above this size the chemical nature of the particles rapidly becomes unimportant and the hydrodynamic interactions, particle shape and geometry dominate the flow. This is also our starting point for particles within the colloidal domain although we will see that interparticle forces are of great importance. 

The major difficulty in predicting the viscosity of these systems is due to the interplay between hydrodynamics, the colloid pair interaction energy and the particle microstructure. Whilst predictions for atomic fluids exist for the contribution of the microstructural properties of the system to the rheology, they obviously will not take account of the role of the solvent medium in colloidal systems. Many of these models depend upon the notion that the applied shear field distorts the local microstructure. The mathematical consequence of this is that they rely on the rate of change of the pair distribution function with distance over longer length scales than is the case for the shear modulus. Thus... 

W.R. Bowen and A.O. Sharif, Hydrodynamic and colloidal interaction effects on the rejection of a particle larger than a pore in microfiltration and ultrafiltration membranes, Chem. Eng. Sci. 53 (1998) 879-890. 

Monte Carlo techniques were first applied to colloidal dispersions by van Megen and Snook (1975). Included in their analysis was Brownian motion as well as van der Waals and double-layer forces, although hydrodynamic interactions were not incorporated in this first study. Order-disorder transitions, arising from the existence of these forces, were calculated. Approximate methods, such as first-order perturbation theory for the disordered state and the so-called cell model for the ordered state, were used to calculate the latter transition, exhibiting relatively good agreement with the exact Monte Carlo computations. Other quantities of interest, such as the radial distribution function and the excess pressure, were also calculated. This type of approach appears attractive for future studies of suspension properties. 

As particle concentration increases, particle interactions and multiple scattering invalidate Eq. (33). The cross terms (y /) in the static and dynamic structure factors. Eq. (29), no longer cancel out, and thus they lead to more complex relationships [l 15-119] for (l>(diffusive motion of interacting particles also becomes more complex, depending on colloidal and hydrodynamic interactions among the particles and their spatial configurations. DLS measurements of particle motion can provide information about suspension microstructure and particle interactions. 

The basic equipment consists of a column packed with stationary, solid beads in the size range 10 to 50 pm [41,42] (Figure 5.8). Means are provided for injecting about 0.2 cm of colloidal suspension, containing about 0.01% polymer by weight, into the flowing stream at the entrance of the column and monitoring the colloid in the column effluent. Particle separation occurs due to a hydrodynamic interaction between the particles and the velocity profile near solid surfaces. HDC is a fast technique but its resolution is low. 

Experimental and theoretical investigations " " " " show that during the approach of two fluid colloidal particles, a flat liquid tihn can appear between their closest regions (see Figure 5.23). The hydrodynamic interactions as well as the buoyancy, the Brownian, electrostatic, van der Waals, and steric forces and other interactions can be involved in film forma-The formation and the evolntion of a foam or emnlsion film usually follows the stages shown in Figure 5.36. 

There are various cases of particle-interface interactions, which require separate theoretical treatment. The simpler case is the hydrodynamic interaction of a solid particle with a solid interface. Other cases are the interactions of fluid particles (of tangentially mobile or immobile interfaces) with a solid surface in these cases, the hydrodynamic interaction is accompanied by deformation of the particle. On the other hand, the colloidal particles (both solid and fluid) may hydrodynamically interact with a fluid interface, which thereby undergoes a deformation. In the case of fluid interfaces, the effects of surfactant adsorption, surface diffusivity, and viscosity affect the hydrodynamic interactions. A special class of problems concerns particles attached to an interface, which are moving throughout the interface. Another class of problems is related to the case when colloidal particles are confined in a restricted space within a narrow cylindrical channel or between two parallel interfaces (solid and/or fluid) in the latter case, the particles interact simultaneously with both film surfaces. 

The Newtonian viscosity of a liquid is modified, and may become non-Newtonian, if it contains colloidal particles. This results from the complex interplay of interactions including hydrodynamic interactions between the liquid and solid particles, attractive or repulsive forces between the particles, and, in concentrated systems, direct particle-particle contact. 

Sometimes when dealing with a fluid that contains a dispersed particle phase that cannot be considered a component, we treat the suspension fluid as a continuum with a constitutive relation that is modified because of the presence of the particles. An example to be discussed in Chapter 5 is Einstein s modification of the Newtonian viscosity coefficient in dilute colloidal suspensions due to hydrodynamic interactions from the suspended particles. As with molecular motions, the modified coefficient may be determined from measurements of the phenomenon itself by using results from analyses of the particle behavior in the fluid as a guide. These ideas are further expanded upon in Chapter 9 where the behaviors of concentrated suspensions of colloidal and non-colloidal particles are examined. 

Up to this point we have considered distributed dilute dispersions of colloidal size particles and macromolecules in continuous liquid media. Where the particles are uncharged and of finite size, they are always separated by a fluid layer irrespective of the nature of the hydrodynamic interactions that take place. In the absence of external body forces such as gravity or a centrifugal field or some type of pressure filtration process, the uncharged particles therefore remain essentially uniformly distributed throughout the solution sample. We have also considered the repulsive electrostatic forces that act between the dispersed particles in those instances where the particles are charged. These repulsive forces will tend to maintain the particles in a uniform distribution. The extent to which a dispersion remains uniformly distributed in the absence of applied external forces, such as those noted above, is described in colloid science by the term stability, whereas colloidal systems in which the dispersed material is virtually insoluble in the solvent are termed lyophobic colloids. 

Consider now coalescence taking into account the molecular and electrostatic forces. Of the greatest interest is dependence of stability factor F on parameters k, //, Sa, Sr, t, y, a, and definition of the criterion for transition from slow to fast coagulation. In Section 11.5 the condition of transition from slow to fast coagulation was considered within the framework of DLVO theory of identical colloid particles without taking into account hydrodynamic interaction... 

A polymer colloid particle will typically contain a substantial number of polymer chains within the particle. These can be arranged in a crystalline, amorphous, rubbery or glassy state. Monomer can also be retained by the particles and hence the particles can be, where the polymer is soluble in the monomer, either extensively or minutely swollen. The physical state of the particle can be important in close-range colloidal and hydrodynamic interactions and in drying processes. For example, if the particles are soft, coalescence of the particles can occur to give continuous film formation, whereas with hard particles their individuality is retained in the dry state. 

To estimate colloidal forces acting between the droplets during the collision, x, z coordinates of the initial (x, Zj) and final (xf, Zf) positions of the mobile droplet before and after the collision are needed. When several pairs of x, z coordinates are plotted on a graph a speeifie seattering pattern will appear. This pattern can be analyzed by eompar-ing the experimental final positions with the ones ealeulated from a theory (2,3), which covers hydrodynamic interactions between the droplets and between the mobile droplet and the wall as well as all external forees aeting on the mobile drop, e.g., those described by DLVO theory. Thus, in the calculations, we assume the existenee of a certain force described by a certain function of the droplet-droplet separation. The final position of the droplet is then calculated and compared with the experimental results. The best match between experimental and theoretical final droplet positions yields the optimum set of parameters or the optimum force-distance profile. 

A unique interaction between fluid mechanics and transport exists for filtration processes. Such processes perform better than expected based on the predicted impact of concentration boundary layers. The improvement in performance, a rare occurrence for membrane processes, arises from a combination of hydrodynamic diffusion and inertial lift [51]. Hydrodynamic interactions between particles or colloids that accumulate in the concentration boundary layer lead to shear-induced diffusion away from the membrane surface. Shear-induced diffusion can be significantly larger than molecular diffusion and thereby reduce surface concentrations. For sufficiently large particles at high shear rates, inertial lift becomes the dominant mechanism for particle movement away from the membrane. 

Abstract. The stability of suspensions/emulsions is under consideration. Traditionally consideration of colloidal systems is based on inclusion only Van-der-Waals (or dispersion) and electrostatic components, which is refereed to as DLVO (Derjaguin-Landau-Verwey-Overbeek) theory. It is shown that not only DLVO components but also other types of the inter-particle forces may play an important role in the stability and colloidal systems. Those contributions are due to hydrodynamic interactions, hydration and hydrophobic forces, steric and depletion forced, oscillatory structural forces. The hydrodynamic and colloidal interactions between drops and bubbles emulsions and foams are even more complex (as compared to that of suspensions of solid particles) due to the fluidity and deformability of those colloidal objects. The latter two features and thin film formation between the colliding particles have a great impact on the hydrodynamic interactions, the magnitude of the disjoining pressure and on the dynamic and thermodynamic stability of such colloidal systems. 

Honig, E.P., Roebersen, GJ. and Wiersema, PH. (1971). Effect of hydrodynamic interaction on the coagulation rate of hydrophobic colloids. J. Colloid Interface Sci.,36,97-109. 

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