Hydrodynamic flows

Hydrodynamic flow depends on the profile of the separation column. If the separation column has a cylindrical shape then, due to the internal friction, there arises a transversal velocity gradient as demonstrated schematically in Fig. 2.3. 

Another velocity distribution occurs when the hydrodynamic flow is caused by capillary forces in a stabilizing flat bed sorbent, when evaporation of the electrolyte from the surface can occur. If this evaporation is not too intensive, it is equal over the whole surface of the sorbent. Concomitantly, with the buffer evaporation from the surface, the buffer solution is supplied from both electrode vessels due to surface forces. Thus, a longitudinal flow originates the velocity of which is a function of the distance. This flow can be made use of in focusing methods [1,9,12,13]. 

Electro-osmotic flow arises when an electric field is imposed into the system. Due to the electric field the spatial charge of the diffusion part of the electric double layer 

The velocity of the osmotic flow through a single capillary with a length of L and 

the volume velocity of the osmotic flow, defined as the volume of the solution transported due to electroosmotic in unit time, is used 

Many of the fundamental concepts and technical solutions used nowadays in microfluidics have been borrowed from the older techniques - continuous flow analysis (CFA) and flow-injection analysis (FIA) [25]. However, the implementation of microfluidic chips has encouraged further miniaturization. Therefore, there have been attempts to scale down the macroscopic fluid handling devices (e.g., peristaltic pumps with footprints of a few square decimeter) to the dimensions of microchips (square millimeters). 

Fluids are often pumped hydrodynamically to exert the flow. Various pumps are used, including syringe pumps, peristaltic pumps, piezoelectric pumps, and gas-pressure-driven hydrodynamic pumps. In the case of hydrodynamic pumps, an inert gas is pressurized in the headspace of the vial containing the sample or carrier fluid. The force exerted by the gas on the liquid phase sustains flow of the liquid in the channel. When a liquid moves along the circular cross-section channel, the Poiseuille equation can be used to relate the 

Alternatively, electrolyte solutions can be moved along microfluidic channels using elec-troosmotic flow (EOF see Chapter 6). In this case, an electric field rather than mechanical force is used to move the liquid. Implementation of EOF allows one to handle the backpressure problem associated with hydrodynamic pumping. However, EOF is mainly used to transport dilute aqueous electrolyte solution, and is sensitive to pH change. 

To characterize the behavior of hydrodynamic flow in microchips, it is helpful to introduce the most important dimensionless parameters. The Reynolds number (Re) is defined as the ratio of inertial to viscous forces acting on the fluid (cf. [7])  

Please note that microfluidics is sometimes defined as the science and technology of systems that process or manipulate small (10 -10 1) amounts of fluids, using channels with dimensions of tens to hundreds of micrometers [7]. Nonetheless, practical dimensions of channels used in many prototype microchips range from 10 pm to 1 mm, and beyond. Thus, the laminar character of flow may vary to some extent even within one microchip that incorporates features with different characteristic dimensions. 

The many different summaries of available data should be consulted for specific interest. The review of Davison and Graham also has a summary of 

---

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

Gonnella G, Orlandini E and Yeomans J M 1997 Spinodal decomposition to a lamellar phase effect of hydrodynamic flow Phys. Rev. Lett. 78 1695... 

If a particularly parallel beam is required in the chamber into which it is flowing the beam may be skimmed in the region of hydrodynamic flow. A skimmer is a collimator which is specially constructed in order to avoid shockwaves travelling back into the gas and increasing 7). The gas that has been skimmed away may be pumped off in a separate vacuum chamber. Further collimation may be carried out in the region of molecular flow and a so-called supersonic beam results. When a skimmer is not used, a supersonic jet results this may or may not be collimated. 

The other mechanism appears in scrubbers. When water vapor diffuses from a gas stream to a cold surface and condenses, there is a net hydrodynamic flow of the noncondensable gas directed toward the surface. This flow, termed the Stefan flow, carries aerosol particles to the condensing surface (Goldsmith and May, in Davies, Aero.sol Science, Academic, New York, 1966) and can substantially improve the performance of a scrubber. However, there is a corresponding Stefan flow directed away from a surface at which water is evaporating, and this will tend to repel aerosol particles from the surface. 

ON-LINE MONITORING OF HYDRODYNAMIC FLOW PROFILES IN MICROFLUIDIC CHANNELS BASED UPON MICROELECTROCHEMISTRY... 

Miniaturisation of various devices and systems has become a popular trend in many areas of modern nanotechnology such as microelectronics, optics, etc. In particular, this is very important in creating chemical or electrochemical sensors where the amount of sample required for the analysis is a critical parameter and must be minimized. In this work we will focus on a micrometric channel flow system. We will call such miniaturised flow cells microfluidic systems , i.e. cells with one or more dimensions being of the order of a few microns. Such microfluidic channels have kinetic and analytical properties which can be finely tuned as a function of the hydrodynamic flow. However, presently, there is no simple and direct method to monitor the corresponding flows in. situ. 

OPTIMISATION OF MICROBAND ELECTRODE SIZES AND LOCATIONS WITHIN A RECTANGULAR MICROFLUIDIC CHANNEL FOR ELECTROCHEMICAL MONITORING OF HYDRODYNAMIC FLOW PROFILES... 

In this chapter the regimes of mechanical response nonlinear elastic compression stress tensors the Hugoniot elastic limit elastic-plastic deformation hydrodynamic flow phase transformation release waves other mechanical aspects of shock propagation first-order and second-order behaviors. 

We expect more insight from simulations in the future, particularly in situations where these multicomponent systems show effects of coupling between the different degrees of freedom, surface tensions depending on temperature and concentration, hydrodynamic flow induced by concentration gradients in addition to thermal buoyancy. 

In Bridgman growth [155], a boat or vessel filled with the melt is slowly cooled from one side, so that the crystal forms from that side. In Czochralski growth [156,157] a cylindrical crystal sits on the surface of the melt and is slowly pulled upward. In both cases the hydrodynamical flow of the melt is an important factor in the chemical composition and fine structure of the resulting crystal. 

The basic model equations for a description of hydrodynamical flow are the Navier-Stokes equations, representing momentum conservation in the fluid... 

J. Fukuda. Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals. Eur Phys J B 7 173, 1998. 

Trinh et al. [399] derived a number of similar expressions for mobility and diffusion coefficients in a similar unit cell. The cases considered by Trinh et al. were (1) electrophoretic transport with the same uniform electric field in the large pore and in the constriction, (2) hindered electrophoretic transport in the pore with uniform electric fields, (3) hydrodynamic flow in the pore, where the velocity in the second pore was related to the velocity in the first pore by the overall mass continuity equation, and (4) hindered hydrodynamic flow. All of these four cases were investigated with two different boundary condi-... 

The volume averaging approach discussed in the section on diffusive transport can also be extended to account for electrophoresis [215] and hydrodynamic flow [215,436]. Locke [215] considered the application of volume averaging to the determination of the effective... 

Under realistic conditions a balance is secured during current flow because of additional mechanisms of mass transport in the electrolyte diffusion and convection. The initial inbalance between the rates of migration and reaction brings about a change in component concentrations next to the electrode surfaces, and thus gives rise to concentration gradients. As a result, a diffusion flux develops for each component. Moreover, in liquid electrolytes, hydrodynamic flows bringing about convective fluxes Ji j of the dissolved reaction components will almost always arise. 

Resulting maps of the current density in a random-site percolation cluster both of the experiments and simulations are represented by Figure 2.9.13(b2) and (bl), respectively. The transport patterns compare very well. It is also possible to study hydrodynamic flow patterns in the same model objects. Corresponding velocity maps are shown in Figure 2.9.13(d) and (c2). In spite of the similarity of the... 

Figure 2 Flow profiles for electro-osmotic and hydrodynamic flows.

---