Water is Flowing Through the Capillaries in Steady Continuous Flow

Capillary Flow

Glass: Sol–Gel Coatings

M. Guglielmi , in Encyclopedia of Materials: Science and Technology, 2001

1.3 Capillary-flow

Flat substrates may be also uniformly coated by the capillary-flow (or laminar-flow) process. The solution is pumped into a horizontal slot application tube or a porous tube from where it flows out on to the surface through the slot or the pores and forms a continuous liquid film on the outside. The substrate is placed in contact with the liquid film and two menisci form. The substrate is moved smoothly relative to the applicator tube and a film is deposited on the wetted surface. This technique is, in principle, similar to dip-coating, but it requires a much smaller reservoir of solution.

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Characterization of Porous Solids VII

S. Galaup , ... M. Dai , in Studies in Surface Science and Catalysis, 2007

3.3. Dynamics of fluid–air capillary flow at the pore-scale

The simplest equation to calculate the dynamics of Fluid–air capillary flow at the pore-scale is attributed to Washburn. It is usually considered to be rigorous for the case of capillary penetration into a uniform capillary tube or bundle of uniform capillary tubes. By combining with the Hagen–Poiseuille equation, the capillary velocity ( v) is given by the following:

(3) $\overline{v}=\frac{dx}{dt}=\frac{dP}{dx}\frac{R^2}{8\eta }\text{with}\left(\text{2}\right),\text{we}\text{obtained}\overline{v}=\frac{R\gamma cos\theta }{4x\eta }$

where x is the length of fluid penetration; dP is the pressure drop between the meniscus and the bulk liquid; R the tube radius; η the fluid viscosity; θ the contact angle and γ is the interfacial tension. This equation relates the rate of meniscus advance at a given length to other physical properties. The capillary velocity is proportional to the raduis R While integrating, we obtained:

(4) $x^2=\frac{Rt\gamma cos\theta }{2\eta }$

The position of the meniscus increase with $\sqrt{t}$ and $\sqrt{R}$ . If there is a distribution of different radii capillary, the liquid will not get in at the same velocity in all radii. Sorbie et al. [17] have re-examined the basis of the Washburn equation and have extended this equation.

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Nanoparticle Technologies

Farid Bensebaa , in Interface Science and Technology, 2013

3.9 Other Forces

Besides electrical and magnetic fields, there are numerous other forces that could provide directional self-assembling [111]. These forces include capillary, flow, special confinements, and gravity. In some cases, capillary forces could play a significant role. Colloidal particles are subjected to capillary forces when the interfaces involve a liquid. This occurs in the case of liquid–gas, liquid–liquid, liquid–solid interfaces [196]. Capillary forces directed normally to the contact line are ascribed to either liquid-in-gas or gas-in-liquid capillary bridges. The lateral capillary forces are parallel to the contact line. This second group of capillary forces is due to the overlap of interfacial deformations created by separate colloidal particles [196]. Two different subclasses of lateral forces are distinguished: flotation and immersion. The deformations in the case of flotation are caused by the particle weight and buoyancy. Immersion includes three different types of deformation (infinite menisci, finite menisci, and capillary multimodes). These deformations are caused by the wetting properties of the particle surface and, in particular, the position and shape of the contact line.

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Biophysical Techniques for Structural Characterization of Macromolecules

S. Mitic , S. de Vries , in Comprehensive Biophysics, 2012

1.22.2.5 Continuous-Flow Instruments

Continuous-flow methods are used in pre-steady-state enzyme kinetic studies and kinetic studies of protein folding. In the continuous-flow experiment, two or more fluids are continuously forced at high flow rates through a mixer, in which they are completely mixed under turbulent flow conditions. The progress of the reaction is then observed at different times under steady-state flow conditions at several distances from the mixer along the flow cell. Monitoring of the reaction is most commonly performed by fluorescence or UV-Vis absorbance spectroscopy. The dead time of continuous-flow instruments is considerably shorter than that of the stopped-flow apparatus; however, the consumption of reagents is much higher. ²³ Reduction of sample amount became possible with advances in mixer design and detection methods. These advancements made it possible to achieve efficient, ultrafast mixing and to acquire a complete kinetic profile in a few seconds.

In 1985, Regenfuss et al. introduced a continuous-flow capillary jet mixer in which the principle of coaxial mixing was combined with the Berger ball mixer (Figures 1(b) and 2(a)). ^29,30,39 The original design of the coaxial ball mixer or capillary micromixer by Regenfuss et al. was impractical because it was delicate and difficult to manufacture, and the progress of the reaction had to be monitored in an unstable, free-flowing jet by measuring fluorescence emission at various distances downstream from the mixer. ⁴¹ Continuous-flow experiments involving a free-flowing jet in general encounter difficulties due to instability of the jet and optical scattering artifacts. ⁸⁰

Shastry et al. successfully overcame the limitations of the Regenfuss continuous-flow capillary mixing apparatus by replacing the glass with a more sophisticated quartz capillary mixer with a fused-silica fluorescence observation flow cell and a custom-made, partially opaque absorbance flow cell, both of which have 0.25   mm path length. ^23,41 The design was further improved by integrating a digital camera with a UV-coated charged coupled device detector into the detection system, which covers almost the entire UV-Vis spectral region (200–1000   nm) (Figure 2(a)). The mixing time of 15   μs and the dead time of 45±5   μs of this mixing apparatus made it possible, for example, to study the kinetics of the early stages of protein folding by recording either the fluorescence profile or the transmittance/absorbance spectra along the whole length of the observation cell (10–15   mm) starting from the dead time to approximately 2   ms.

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Thinning Films and Tribological Interfaces

K Walters , in Tribology Series, 2000

5 THE PRESSURE DEPENDENCE OF η_E

In view of the previous discussion, there is clearly a need to study the pressure dependence of all the rheometrical functions which are routinely measured, being careful to attain pressures of relevance to lubrication. The University of Wales Institute of non-Newtonian Fluid Mechanics is investing significant resources into the general problem, but some preliminary experiments on the pressure dependence of η_E have been enlightening ( 22 ). These have involved capillary flow and, in particular, the pressure loss in the contraction region before the usual capillary test section.

In view of the general difficulty of determining η_E for mobile elastic liquids, we have argued in favour of those devices which provide simple means of determining resistance to extensional deformation and which can yield an extensional viscosity if not the extensional viscosity. In that spirit, we have adapted a capillary viscometer to work at high pressure by simply applying a back pressure at the capillary exit. Using ideas pioneered by Cogswell ( 23 ) and Binding ( 24 ), it is possible to interpret the pressure loss in the contraction zone before the capillary in terms of an extensional viscosity. The basic capillary flow is, of course, able to supply the important shear viscosity.

To illustrate the utility of the technique, we show in Fig 10 data for a single grade oil. We define the Trouton ratio by (cf. 25 )

Figure 10. Trouton ratio data for a single grade oil at 0, 40 and 80 MPa.

(17) $T_R=\frac{{\eta }_E\left(\dot{\epsilon }\right)}{\eta \left(\sqrt{3}\dot{\epsilon }\right)}\text{.}$

This removes the ambiguity in assigning values to both extensional strain rate and shear rate and at the same time ensures T_R   =   3 for all $\dot{\epsilon }$ , unless viscoelasticity is affecting the extensional viscosity response. Note that the data in Fig 10 imply that there is no discernible effect of pressure, with values of T_R as close to the Newtonian value as one can reasonably expect from the technique.

To demonstrate the most important findings of the Binding et al ( 22 ) work, we show in Fig 11 representative shear viscosity and extensional viscosity data for an oil in the IOW/40 category. The shear viscosity at the three pressures shows typical shear thinning behaviour and the extensional viscosity exhibits tension thickening, which is again not unexpected for polymeric fluids. When the results are replotted in terms of the Trouton ratio, we obtain the dramatic results shown in Fig 12. In contrast to the data for the single grade oil, which are also shown in the Figure, we see a strong pressure dependence of T_R in the case of the multigrade oil. This means that the extensional viscosity is a stronger function of pressure than the shear viscosity in this case. Note also that, for all pressures, T_R iss significantly higher than the Newtonian value of 3, another indication of a strong viscoelastic response.

Figure 11. Shear viscosity (solid symbols) and extensional viscosity (open symbols) for a multigrade oil at 0, 40 and 80 MPa.

Figure 12. Trouton ratio data for a multigrade oil and a single grade oil at 0, 40 and 80 MPa.

(From Reference 22 .)

We are in the process of extending our pressure work to the dynamic viscosity η′ and dynamic rigidity G′. On the basis of the η_E data, we would not be surprised if G′ exhibited a stronger dependence on pressure than η′!

So, the experimental data to hand seems to suggest that the pressure dependence of those rheological functions which can be associated with viscoelasticity could be stronger than that for the shear viscosity.

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Processing Aid Removal

J.A. Lewis , in Encyclopedia of Materials: Science and Technology, 2001

2.2 Liquid Redistribution Processes and Scaling Criteria

Capillary forces may act to redistribute thermoplastic binders within the porous network of ceramic green bodies in a manner analogous to drying compacts (Lewis and Cima 1990, Barone and Ulicny 1990, Sproson and Messing 1988, Cima et al. 1989a, 1989b ). A model that equates the driving force for capillary flow to the viscous pressure drop resulting from flow through a fully saturated porous body is given by

(1) $\frac{h}{d}=\frac{\text{Δ}\varphi {\varepsilon }^3}{18K{(1-\varepsilon )}^2}\frac{\gamma }{vG}$

where h is the maximum length scale over which capillary forces act, d is the particle diameter, γ is the surface tension of the binder phase, ν (=μ/ρ) is the kinematic viscosity, G is the mass flux, ɛ is the void fraction of the porous body, and K (≈ 5) is a constant that accounts for geometrical factors of the pores, such as their tortuosity and number of constrictions. Close packing of equally sized spheres produces the smallest pores, with ϕ=12.9, whereas a simple cubic arrangement of spheres has larger pores, with ϕ=4.8. Thus, Δϕ=(12.9−4.8)≈8, which represents a conservative estimate of the capillary driving force since packing in the least-dense areas of the ceramic green body will be likely to be less dense than cubic packing. The right-hand side of Eqn. (1) indicates that the characteristic distance, h, over which capillary-driven liquid migration occurs increases with increasing surface tension. Correspondingly, h decreases as the viscosity and/or mass flux increases since viscous losses become more important.

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Blood Flow Through Capillary Networks

C. Pozrikidis , J.M. Davis , in Transport in Biological Media, 2013

6.4.8 Significance of the Bifurcation Law

An important objective of the simulations is to clarify the significance of the cell partitioning law at divergent bifurcations. For this purpose, simulations were performed on a $32\times 17$ network whose nodes are perturbed with amplitudes ${∊}_x={∊}_y=0.5$ , for uniform capillary radii, ${∊}_a=0$ . The Klitzman and Johnson law (6.20) with a specified value of the exponent, q, was used at diverging bifurcations. Results for the capillary discharge hematocrit obtained using the standard parameters stated in Section 6.4.4 for inlet hematocrit ${(H_D)}_{\text{in}}=0.4375$ are represented by the plus (+) symbol in Fig. 6.10a.

Figure 6.10. (a, b) Effect of the cell partitioning-law exponent, q, on the capillary discharge hematocrit of a $32\times 17$ lattice for inlet hematocrit ${(H_D)}_{\text{in}}=0.4375$ , node perturbation amplitude ${∊}_x={∊}_y=0.5$ and capillary radius perturbation amplitude (a) ${∊}_a=0$ or (b) $0.10$ . (c, d) Same as (a, b) but for inlet hematocrit ${(H_D)}_{\text{in}}=0.2188$ .

When q  = 1, all segments have the same discharge hematocrit, equal to the inlet hematocrit, even though the capillary flow rates are not the same. As q increases, the range of variation of the hematocrit considerably widens inside a nearly linear envelop. The iterative solution procedure fails to converge approximately when $q>4.5$ due to the exceedingly high discharge hematocrit of certain segments. The discharge hematocrits obtained using the empirical correlation (6.23) are represented by the $\times$ symbol near the right vertical frame in Fig. 6.10a. The data vary in a range corresponding to $q\simeq 1.5$ . This value of q may be regarded as typical of homogeneous physiological networks.

The simulations confirm that the bifurcation exponent, q, has a profound effect on the distribution of the discharge hematocrit. The effect becomes more pronounced when the capillary tubes are assigned different radii, as shown in Fig. 6.10b for ${∊}_a=0.10$ . In this case, the critical value of q below which the calculations fail to converge decreases to approximately 4.0. Simulations for lower inlet hematocrits reveal similar behavior, as shown in Fig. 6.10c and d for inlet hematocrit ${(H_D)}_{\text{in}}=0.2188$ . When $q=4.5$ , some capillary segments are nearly entirely devoid of cells.

A direct visual impression of the broad range of the discharge hematocrit at high values of q can be obtained from Fig. 6.11a for a $16\times 9$ randomized network. The thickness of the capillary segments shown in this figure scales with the capillary discharge hematocrit. For example, the thicknesses of all inlet segments at the bottom of the test section are all the same. The Klitzman and Johnson partitioning law (6.20) with $q=4.5$ is employed at divergent bifurcations. Close inspection reveals capillary pathways connecting the inlet to the outlet. These pathways are reminiscent of percolation paths in damaged networks (e.g., [27]). Corresponding results are shown in Fig. 6.11b where the Pries et al. correlation (6.23) is employed. Close inspection reveals that the discharge hematocrit is distributed more uniformly across the capillary network.

Figure 6.11. Flow in a $16\times 9$ network with ${∊}_x=0.5\text{,}{∊}_y=0.5\text{,}{∊}_a=0.10$ , for inlet hematocrit ${(H_D)}_{\text{in}}=0.2188$ . The Klitzman and Johnson law (6.20) with $q=4.5$ is employed in (a) and the Pries et al. law (6.23) is employed in (b). The thickness of the capillary segments in the illustrations scales with the capillary discharge hematocrit.

Similar results were obtained for conditions other than the standard conditions discussed in Section 6.4.4. This includes different reference capillary blood velocities and different mean capillary radii. The results presented in this section are typical of flow through the model network under physiological conditions.

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Biochemical Applications of Raman Spectroscopy*

Peter Hildebrandt , Sophie Lecomte , in Encyclopedia of Spectroscopy and Spectrometry (Second Edition), 1999

Dynamics of Biomolecules

Operating in the time-resolved domain, RR spectroscopy can be employed to probe the dynamics of biological systems. Hence, such studies can provide simultaneously kinetic and structural data. In many cases, time-resolved RR spectroscopy, albeit technically demanding, may represent the method of choice for elucidating the molecular mechanisms of biological reactions.

Photoinduced Processes

Bacterial retinal proteins such as bacteriorhodopsin and halorhodopsin act as light-driven ion pumps. The ion gradient that is generated across the membrane is then converted into chemical energy (i.e. synthesis of adenosine triphosphate). The ion translocation is linked to a photoinduced reaction cycle of the retinal chromophore. The photophysical and kinetic properties as well as the stability of this class of proteins make them an ideal system for time-resolved RR spectroscopic studies. Moreover, these proteins represent suitable objects for developing and optimizing time-resolved spectroscopic techniques. The main advantage is the reversibility of the photoinduced reaction cycle, that is the system comes back to the parent state in a few milliseconds after the primary photochemical event. Thus, time-resolved RR spectra can be accumulated continuously since the 'fresh sample' condition is readily established. This condition ensures that the protein is always in the same state when irradiated by the exciting laser beam.

There are two approaches for time-resolved RR spectroscopy of these retinal proteins. Using CW-excitation, a time resolution down to 100 ns can be achieved by rapidly moving the sample through the laser focus (rotating cell, capillary flow system). Pulsed laser excitation can provide a time resolution even in the sub-picosecond range depending on the pulse width of the laser. In both methods, intermediate states are probed in dual-beam experiments with the probe beam irradiating the sample after a delay time δ with respect to the photolysis beam which initiates the reaction cycle. The systematic variation of δ allows the determination of the photocycle kinetics which, along with the structural data derived from the RR spectra, can provide a comprehensive picture of the dynamics of the protein. Figure 3 shows a selection of time-resolved RR of halorhodopsin. The bands displayed in these spectra are diagnostic for the retinal configuration (C=C stretching) and confirm that the photoreaction includes the isomerization from the all-trans to the 13-cis configuration.

Figure 3. Time-resolved RR spectra of halorhodopsin from Natronobacterium pharaonis obtained in single (probe only, 514   nm) and dual-beam experiments with variable delay times δ of the probe laser (514   nm) relative to the pump laser (600   nm).

Redox Processes

Cytochrome c oxidase, a membrane-bound enzyme in the respiratory chain of aerobic organisms, reduces oxygen to water. This process which takes place at the binuclear metal centre constituted by a haem a ₃ and a Cu ion runs via several intermediate states with life times in the micro- and millisecond range. Technical improvements now make it possible to monitor this reaction sequence by time-resolved RR spectroscopy using rapid flow systems. The starting point of the experiments is the thermally stable carbon monoxide complex of the reduced enzyme in oxygen-saturated solution. This complex is photodecomposed by a laser beam so that oxygen can bind to the catalytic centre constituting the time 'zero' of the reaction sequence. The various intermediates are probed by a second laser beam irradiating the (photolysed) sample volume after a delay time. The oxygen-sensitive vibrational modes which can readily be identified based on the ¹⁸O/¹⁶O isotopic shifts give insight into the nature of the various intermediates and, hence, into the molecular mechanism of the oxygen reduction. A particularly interesting technical approach for these studies is based on an artificial cardiovascular device designed to maintain a continuous enzymatic reaction. Thus, it is possible to accumulate the RR signals during a sufficiently long period of time using a minimum amount of sample.

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Semiconductor Chip Underfill Materials

S.L. Buchwalter , in Encyclopedia of Materials: Science and Technology, 2001

2 Underfill Material Properties

To meet both processing and device protection requirements, underfill materials must have a variety of properties both in the uncured and cured states (Suryanarayana et al. 1993, Wang and Papathomas 1993, Koh and Ryan 1995). Some of the most important are reviewed below.

2.1 Composition

Commercial underfills are proprietary compositions from various material suppliers. Epoxy thermosetting resins are the predominant materials, but other thermosets such as cyanate esters are also used. Underfills are formulated as 100% solids compositions, i.e., liquid resins and hardeners are used without solvents or volatile additives. Thermal curing of these compositions generates a hard plastic material without appreciable weight loss.

2.2 Filler

Underfills are commonly formulated with 60–70% by weight of amorphous, fused silica. The silica is used to reduce the CTE of the underfill material because without filler the CTE of the cured polymer would cause unacceptable solder joint strain. Generally, underfill formulations have CTEs of 25–30   ppm°C⁻¹, which closely approximates to that of solder.

Fillers, if not chosen carefully, can increase the viscosity of the formulation to the point that it will not flow under the chip to fully encapsulate the solder joints. For this reason, a special class of high-purity, spherical silica of controlled particle size distribution has been developed for underfills. Using these fillers, underfills typically are formulated to have room-temperature viscosities of 5×10³–1×10⁴  cPs (5–10   kgm⁻¹s⁻¹ ), which allow encapsulation of the solder joints by capillary flow at a rate acceptable for manufacturing.

2.3 Cure

Underfills are formulated as thermosets rather than thermoplastics, primarily because the viscosity of solvent-free, high-performance thermoplastics is much too high for the encapsulation process. As thermosets, underfills have to be cured by heating after encapsulation, and full cure is essential to optimize properties such as adhesion, glass transition temperature (T _g), and modulus. Manufacturing throughput considerations demand short cure cycles, preferably compatible with in-line processing. However, most underfills are cured in batch curing ovens at about 150 °C for one hour or more to assure acceptable reliability of the packages.

2.4 Glass Transition Temperature (T_g)

The glass transition temperature of a polymer is the temperature region of the change from a rigid "glassy" state to a flexible "rubbery" state. Most properties of thermosets, including underfills, undergo step changes at T _g. For example, the modulus of a cured underfill decreases more than ten-fold above T _g as do the cohesive and adhesive strengths. Electrical properties, heat capacity, and chemical resistance also all decrease above T _g. Accordingly, the T _g of cured underfills should be higher than any temperature experienced by the package in the field.

2.5 Elastic Modulus

The function of an underfill is to link mechanically the silicon chip to its carrier, creating a structure that eliminates or drastically reduces the strain on the individual solder joints. The optimum modulus will depend on the application, and is affected by the difference in CTE of the chip and chip carrier, the modulus of the chip carrier, and the CTE of the underfill. A typical value for underfill modulus is about 9   GPa (1.3   Mpsi) at 25 °C.

2.6 Adhesion

Underfill adhesion is the most important property for maintaining reliability of flip chip assemblies. Without durable adhesion, the solder joint reinforcement provided by the underfill is short-lived because as soon as the underfill loses adhesion to one or more surfaces, the thermal stresses are transferred directly to the solder joints. An underfill must have good adhesion to multiple surfaces: the chip passivation, the edges of the silicon chip, the surface of the chip carrier, and the solder itself. Adhesion must also be maintained despite exposure to moisture and thermal stressing.

Adhesive properties of polymers are often affected by moisture. As a small, polar molecule, water easily diffuses through polymers and can adsorb at an interface, disrupting adhesive bonding. The microelectronic packaging industry has developed a set of criteria to classify the resistance of packages to moisture effects, called JEDEC levels 1–5 (JEDEC 1995). The levels differ in the aggressiveness of the moisture stress, which precedes other reliability testing such as simulated solder reflow and thermal shock testing.

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Introduction

Jean-Pierre Hansen , Ian R. McDonald , in Theory of Simple Liquids (Third Edition), 2006

1.3 EXPERIMENTAL METHODS

The experimental methods available for studying the properties of simple liquids may be placed in one of two broad categories, depending on whether they are concerned with measurements on a macroscopic or microscopic scale. In general, the calculated microscopic properties are more sensitive to the approximations used in a theory and to the assumptions made about the pair potentials, but the macroscopic properties can usually be measured with considerably greater accuracy. The two types of measurement are therefore complementary, each providing information that is useful in the development of a statistical-mechanical theory of the liquid state.

The classic macroscopic measurements are those of thermodynamic properties, particularly of the equation of state. Integration of accurate P–ρ–T data yields information on other thermodynamic quantities, which can be supplemented by calorimetric measurements. For most liquids the pressure is known as a function of temperature and density only in the vicinity of the liquid–vapour equilibrium line, but for certain systems of particular theoretical interest experiments have been carried out at much higher pressures; the low compressibility of a liquid near its triple point means that highly specialised techniques are required. The second main class of macroscopic measurements are those relating to transport coefficients. A variety of experimental methods are used. The shear viscosity, for example, can be determined from the observed damping of torsional oscillations or from capillary-flow experiments, while the thermal conductivity can be obtained from a steady-state measurement of the transfer of heat between a central filament and a surrounding cylinder or between parallel plates. A direct method of determining the coefficient of self-diffusion involves the use of radioactive tracers, which places it in the category of microscopic measurements; in favourable cases the diffusion coefficient can be measured by nuclear magnetic resonance (NMR). NMR and other spectroscopic methods (infrared and Raman) are also useful in the study of reorientational motion in molecular liquids, while dielectric-response measurements provide information on the slow, structural relaxation in supercooled liquids near the glass transition.

Much the most important class of microscopic measurements, at least from the theoretical point of view, are the radiation-scattering experiments. Elastic scattering of neutrons or x-rays, in which the scattering cross-section is measured as a function of momentum transfer between the radiation and the sample, is the source of our experimental knowledge of the static structure of a fluid. In the case of inelastic scattering the cross-section is measured as a function of both momentum and energy transfer. It is thereby possible to extract information on wavenumber and frequency-dependent fluctuations in liquids at wavelengths comparable with the spacing between particles. This provides a very powerful method of studying microscopic time-dependent processes in liquids. Inelastic light-scattering experiments give similar information, but the accessible range of momentum transfer limits the method to the study of fluctuations of wavelength of order 10⁻⁵ cm, corresponding to the hydrodynamic regime. Such experiments are, however, of considerable value in the study of colloidal dispersions and of critical phenomena.

Finally, there are a range of techniques of a quasi-experimental character, referred to collectively as computer simulation, the importance of which in the development of liquid-state theory can hardly be overstated. Simulation provides what are essentially exact results for a given potential model; its usefulness rests ultimately on the fact that a sample containing a few hundred or few thousand particles is in many cases sufficiently large to simulate the behaviour of a macroscopic system. There are two classic approaches: the Monte Carlo method and the method of molecular dynamics. There are many variants of each, but in broad terms a Monte Carlo calculation is designed to generate static configurations of the system of interest, while molecular dynamics involves the solution of the classical equations of motion of the particles. Molecular dynamics therefore has the advantage of allowing the study of time-dependent processes, but for the calculation of static properties a Monte Carlo method is often more efficient. Chapter 2 contains a brief discussion of the principles underlying the two types of calculation.

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