Liquid media hydrodynamics

In electrokinetic phenomena such as electroacoustics, theoretical models need to consider the induced movement of charge within the electrical double layer (EDL), the surface current , Is, as well as the interaction of the outer portion of the double layer with the applied signal (acoustic or electric field) and with the liquid medium. Hydrodynamic flows generate surface current as liquid moving relative to the particle... 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

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. 

In a real situation, the motion of the segments of a chain relative to the molecules of the solvent environment will exert a force in the liquid, and as a consequence the velocity distribution of the liquid medium in the vicinity of the moving segments will be altered. This effect, in turn, will affect the motion of the segments of the chain. To simplify the problem, the so-called free-draining approximation is often used. This approximation assumes that hydrodynamic interactions are negligible so that the velocity of the liquid medium is unaffected by the moving polymer molecules. This assumption was used in the model developed by Rouse (5) to describe the dynamics of polymers in dilute solutions. 

Liquid space surrounding active solid. Particularly in heterogeneous reaction system involving a liquid medium, thorough examination of the hydrodynamic flow conditions is appropriate. An example will illustrate this point. 

In the preliminary experiment for MAFF clone 1 in liquid culture using a 100 ml flask, the ratio of UC to DT tended to increase with the increase of rotation rates. In the case of Cephaelis ipecacuanha (section 1.4.2), the frequency of adventitious shoot formation on intemodal segments was 83.7% when cultured in a RDF, whereas it is below 30% when cultured in an airlift type fermenter. The inhibition of shoot formation might be related with the hydrodynamic stress produced by aeration and/or rotation. Therefore, a RDF was chosen for P. somniferum cultures because the production of DT seemed to be associated with the codeine formation. Since moderate growth and alkaloid accumulation and proliferation of DT were observed in WP medium, DT was cultured using WP liquid medium. 

In addition to the surface forces (see Section 5.4 above), two colliding particles in a liquid medium also experience hydrodynamic interactions due to the viscous friction, which can be rather long range (operative even at distances above 100 nm). The hydrodynamic interaction among particles depends on both the type of fluid motion and the type of interfaces. The quantitative description... 

Here we observe that the adhesive force (or detaching force) varies inversely with the time during which the dust-covered surface is held in the liquid medium (or the time during which the detaching force is applied). Such a relationship, hoever, persists only over a limited period of time, subsequently breaking down. This means that the time required to establish the equilibrium thickness of the liquid interlayer depends not only on the hydrodynamic factor, which involves influx and efflux of liquid in the gap between bodies, but also on other factors. 

Another factor that may affect the rheology of emulsions is the viscosity of the disperse droplets. This is particularly the case when the viscosity of the droplets is comparable to or lower than that of the dispersions medium. This problem was considered by Taylor (17), who extended the Einstein hydrodynamic treatment for suspensions for the case of droplets in a liquid medium. Taylor (17) assumed that the emulsifier film around the droplets would not prevent the transmission of tangential and normal stresses form the continuous phase to the disperse phase and that there was no slippage at the o/w interface. These stresses produce fluid circulation within the droplets, which reduces the flow patterns around them. Taylor derived the following expression for 11 ... 

For hard sphere systems, experimental data for the relative viscosity tir (equal to the viscosity of the suspension ti divided by the viscosity of the liquid medium -qo) versus Pg lie on curves of the form illustrated in Fig. 4.37. At low strain rates when is 1, the structure of the suspension is not significantly altered by the shear because Brownian motion dominates over the viscous forces. At higher strain rates, the viscous forces start to affect the suspension stracture, and shear thinning occurs. At very high strain rates, i.e., when P is 1, the viscous forces dominate and the plateau region represents the viscosity of a suspension with a hydrodynamically controlled structure. 

On the basis of the material so far considered, we may suppose that the hydrodynamic factor operates in a liquid medium during the initial period of particle adhesion, i.e., in the case of kinetic adhesion. As the particles approach the surface, the liquid is forced out and the layer between the contiguous bodies is reduced to an equilibrium thickness this corresponds to a transition from kinetic to static adhesion. In the case of air dusting with subsequent placing of the dust-laden sample in the liquid medium, the contact zone is wetted and filled with liquid, forming a liquid interlayer of equilibrium thickness. 

Physico-chemically the bacterial adhesion to a polymer can be regarded as the adhesion of a colloid particle to a solid surface in a liquid environment. Besides the hydrodynamic conditions of the liquid medium which regulate the transport of the particle to the surface, the adhesion IS governed by attractive or repulsive forces including electrostatic, van der Waals, dipole-dipole and hydrophobic interactions.23 Provided... 

In suspensions, it is common to consider particles whose sizes range down to the submicron scale, where Brownian motion and colloidal forces have pronounced effects (Russel et al. 1991). The influence of Brownian motion relative to shear flow is captured through a P clet number given by Pe = ( fl )/Do = (67tTioy )/fcT, where Do = kT/ 6ny Qa) is the Stokes-Einstein diffusion coefficient, k is Boltzmann s constant, and T is the temperature. The first form shows that Pe may be interpreted as a ratio of the hydrodynamic diffusion scaling with the shear rate and particle size ya ) as well as a dimensionless function of the volume fraction not shown. It is more common, however, to interpret Pe as the ratio of a diffusive timescale u IDq, relative to the flow timescale given by When Pe = 0, a Brownian suspension will approach a true equilibrium state through its thermal motions. Interparticle forces of many sorts are possible in a liquid medium. 

Note that filter aid selection must be based on planned laboratory tests. Guidelines for selection may only be applied in the broadest sense, since there is almost an infinite number of combinations of filter media, filter aids, and suspensions that will produce varying degrees of separation. The hydrodynamics of any filtration process are highly complex filtration is essentially a multiphase system in which interaction takes place between solids from the suspension, filter aid, and filter medium, and a liquid phase. Experiments are mandatory in most operations not only in proper filter aid selection but in defining the method of application. Some general guidelines can be applied to such studies the filter aid must have the minimum hydraulic resistance and provide the desired rate of separation an insufficient amount of filter aid leads to a reduction in filtrate quality — excess amounts result in losses is filtration rate and it is necessary to account for the method of application and characteristics of filter aids. 

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