- Email: [email protected]
Overflowing cylinder for neutron reflection research at expanding surfaces
Physica B 283 (2000) 278}281
Over#owing cylinder for neutron re#ection research at expanding surfaces M. Wagemaker *, F.J.G. Boerboom, H.J. Bos, A.A. van Well Interfacultair Reactor Instituut, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands Department of Food Science, University of Wageningen, The Netherlands Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands
Abstract An over#owing cylinder (OFC) suitable for neutron re#ection (NR) was designed to combine the both techniques. The two main requirements for the design are; "rstly, the expanding surface dimensions should be large enough to perform NR, secondly, the vertical dimensions should be minimized because generally there is no space for a long in#ow of the OFC (necessary to guarantee a stable-steady-state expanding liquid surface). The vertical in#ow dimensions are minimized using the design of a circular in#ow plate with a calculated perforation distribution ensuring a cylindricalsymmetric in#ow. Measurements show that the surface #ow of the designed cylinder has the required properties to study the dynamical air}liquid interface. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ha; 87.14.Ee; 79.60.Dp Keywords: Neutron re#ectometry; Over#owing cylinder technique; Protein adsorption; Expanding surface; b-casein
1. Introduction The study of the dynamic adsorption behaviour of surfactant solutions is of great interest for numerous technological processes such as foaming and emulsi"cation [1]. In understanding the stabilising properties of the adsorbed surfactant layer, there exists much interest in the dynamical properties and microscopic structure of these layers. The over#owing-cylinder (OFC) technique provides a method to study the dynamical surface behaviour of adsorbed layers in a steady state [2,3]. In this dynamical system, surface properties, such as surface tension and surface concentration, are determined as a function of the relative rate of surface expansion. The relative rate of expansion is, in case of large molecules like proteins, a measure of time scale for the unfolding of
* Corresponding author. Tel.: #31-15-278-6774; fax: #3115-278-6422. E-mail address: [email protected] (M. Wagemaker)
the adsorbed molecules, e.g., with larger expansion rates, the earlier stage of unfolding is probed [4]. In the last decade the neutron re#ection (NR) technique has been established to be a useful method for studying the depth-dependent atomic density structure in the order of nanometers [5]. The sensitivity of the neutron for hydrogen and the contrast for the neutron between hydrogen and its isotope deuterium, imply that NR o!ers an opportunity to determine the adsorbed surfactant layer structure. Many NR studies of static adsorbed layer structures have recently been performed, but these static studies are not su$cient to explain the behaviour of adsorbed layers at the non-equilibrium (or dynamical) air}water interface such as in foams and emulsions. The combination of the OFC technique and NR would relate the macroscopic quantities to the microscopic properties of the adsorbed layer, i.e. the (dynamic) structure of the layer. This combination would be a step forward in detailed understanding of the stabilising mechanism of adsorbed surfactant layers e.g. proteins. Existing over#owing cylinders are not suitable for NR experiments for two reasons. Firstly, the existing
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 0 0 1 - 3
M. Wagemaker et al. / Physica B 283 (2000) 278}281
over#owing cylinders have a relatively long vertical conical formed cylinder to ensure a laminar #ow"eld, but generally there is only limited vertical space in the experimental set-up of neutron re#ectometers. Secondly, the surface of the existing over#owing cylinders is too small to re#ect enough neutron intensity. Here we present the newly designed OFC that overcomes the two drawbacks but nevertheless ensures a cylindrical symmetric expanding surface #ow. The performance of the NR OFC will be illustrated with measurements on b-casein, a milk protein that has been subject of several studies [4,6,7].
2. Design Fig. 1 shows a cross section of the designed OFC for NR constructed of PMMA. The vertical dimension was decided to be 130 mm, and the OFC radius 90 mm (compare with 40 mm for a conventional OFC). For protein adsorption the relative surface expansion rate is inversely proportional to the time proteins have to unfold at the air}water interface. The relative expansion rate of the surface A is de"ned as [2,3]; dln A/dt"v(r)/r#dv(r)/dr,
(1)
where r is the radius and v(r) the radial velocity. To be scienti"cally interesting the cylinder should provide a range of the relative surface expansion rate, dln A/dt, large enough to probe the adsorbing mechanism at time scales in the order of 0.1 up to 10 s. To perform meaningful NR experiments the probed surface should have a homogenous structure along the re#ecting surface. Assuming that this is true for a constant relative expansion rate and given Eq. (1) the radial velocity, v(r), should be linear in the radius up to a value that allows a large enough neutron beam footprint. The #ow "eld in the central cylinder should be free of rotations and cylindrical symmetric. Because of the
limited vertical space (130 mm) the in#ow-tube is connected to the side-wall of the in#ow compartment, and thus, as can be expected, will not lead to the desired #ow characteristics in the central cylinder where the liquid rises to the expanding surface. To achieve the required #ow a circular plate was designed with a perforation density that distributes the in#ow equally around the cylinder. This can be done by either varying the perforation diameter or the distance between the perforations (perforation density). The latter method was applied for this is technically more straightforward. To calculate this distribution of mutual perforation distances, it was necessary to determine the pressure distribution in the annular region outside the perforated plate (inside the instream compartment). For reasons of simplicity, it has been assumed that the total pressure in the #ow "eld is the assembly of two components, a static pressure and a stagnation pressure. For the total pressure applies: p "ov#p
(2)
where p is the total pressure, p the static pressure, o the density and v the #ow velocity. Due to friction e!ects with the wall the total pressure will decrease with the #ow along the annulus. The loss in total pressure due to friction is, over a length ¸ with a hydraulic radius R (7.5 mm for the in#ow compartment section of 20;60 mm) and using the Poisseulle friction coe$cient for laminar #ow [8]: *p "32gR\¸v
(3)
where g is the liquid viscosity. The in#uence of the curvature of the in#ow compartment on the #ow can be neglected taken the maximum liquid velocity that will be applied. The #ow-rate through a perforation is determined by the pressure di!erence across the perforation, i.e. the di!erence between inside p and outside p of the perfor ated plate, and the drag coe$cient of the perforation, c " ("0.86 for 1 mm diameter perforations [8]): p!p "c ou, "
Fig. 1. Cross-section of the over#owing cylinder designed for neutron re#ectometry studies.
279
(4)
where p (assumed constant) is the pressure at the main cylinder side of the circular plate and u the liquid velocity through the perforation. Applying Eqs. (2)}(4) and the requirement of a constant in#ow per unit length in the #ow direction, leads to the speci"c perforation distribution that should provide a rotation free and cylindrical symmetric #ow"eld in the central cylinder. In addition to prevent rotation, radial-directed plates have been placed in the main compartment.
280
M. Wagemaker et al. / Physica B 283 (2000) 278}281
The plate designed for the presented cylinder was constructed of PVC (length 1002 mm, width 60 mm and thickness 1 mm) with 72 rows of 10 perforations 2.5 mm in diameter. The distance between the rows of perforations was calculated for one half of the plate (the #ow is symmetric left and right of the in#ow) and increased downstream starting with 5.5 mm at the in#ow up to 20.0 mm opposite of the circular placed plate. The liquid trajectory through the OFC system is as follows (Fig. 1); the liquid enters the circular in#ow compartment from where it is equally distributed, through the calculated perforation distribution, in the main cylinder. After the liquid enters the main cylinder it rises through the central cylinder and eventually #ows over the rim into the collecting cylinder. From there it is pumped back to the in#ow compartment, via a decoupled system to prevent vibrations that could disturb to the expanding liquid surface.
Fig. 2. Radial surface velocity v(r) as a function of the surface #ow radius for two concentrations b-casein, 0.3 and 1.0 g/l, for each concentration for two falling "lm lengths H , at constant #ow rate Q"40 cm/s.
3. Performance The b-casein used in the experiments was purchased from Eurial Produits Industriels and dissolved in demineralised water. The pH of the aqueous solution was stabilised at 6.7 with a 75 mmol/l Na HPO /KH PO solution. To prevent bacteria growth 0.2 g/l NaN was added. For two b-casein concentrations the wetting "lm length H was varied at a constant #ow rate Q" 40 cm/s. Note that only the values of the #ow rate and the length of the wetting "lm (H in Fig. 1) can be imposed on the liquid over#owing cylinder system. The other parameters are determined autonomously by the system [2,3]. The radial velocity v(r) of the expanding surface was measured using Laser Doppler Anemometry (LDA) [9]. The expanding surface #ow, v(r), showed to be free of rotations and cylindrical symmetric. For two b-casein concentrations the radial velocity v(r) and the relative surface expansion rate dln A/dt were measured as a function of wetting "lm length H , as shown in Figs. 2 and 3, respectively. The relative expansion rate, dln A/dt, can be directly determined out of v(r) using Eq. (1). For the OFC, the driving mechanism of the expanding surface for surfactant solutions was concluded to be the surface tension gradient generated by the free falling part of the wetting "lm [2,3]. Above a certain wetting "lm length the free falling part does not increase and is consequently not able to increase the relative expansion rate as can be seen in Fig. 3 for the newly designed OFC. Up to a certain "lm length the relative expansion rate is zero. This is assumed to be the result of a rigid b-casein "lm (held together by lateral interactions) build up on the surface and extending into the free falling part of the wetting "lm [4]. Such a "lm is able to resist the shear stress between the bulk #ow and the protein "lm and thus keeping the relative expansion rate to zero.
Fig. 3. Relative expansion rate, dln A/dt, as a function of the wetting "lm length, H , at constant #ow rate Q"40 cm/s for two concentrations b-casein, 0.3 and 1.0 g/l.
The range of dln A/dt, a measure of adsorption time window, is large enough to in#uence the properties of the adsorbing protein molecules strongly. Therefore, the newly designed cylinder o!ers a large enough range in dln A/dt to be interesting in studying the mechanical properties of adsorbing proteins such as b-casein. For NR experiments the probed surface should have a homogenous structure along the re#ecting surface. Therefore the relative expansion rate should be constant over a large enough expanding surface de"ned by the radius. For the low surfactant concentration this is not a problem, v(r) is linear in r at least up to 60 mm (conform Fig. 2 and Eq. (1)), for the high concentration in combination with a large wetting "lm length, the linear region becomes very limited. The strong non-linear behaviour at relatively small radii compared to conventional cylinders could be caused by the di!erence of the #ow properties in the central cylinder. For the conventional cylinder it was observed to be laminar (parabolic velocity pro"le) [2,3] and for the NR OFC it was observed to be more like a crop-#ow. We conclude that the designed over#owing cylinder described in this paper satis"es the demand that it generates a tuneable expanding surface properties comparable with conventional over#owing cylinders. For high concentrations surfactant one has to consider the nonlinearity of the radial velocity pro"le. First experiments with this OFC are successfully performed at the
M. Wagemaker et al. / Physica B 283 (2000) 278}281
re#ectometer SURF at ISIS in a study to the adsorption mechanism of b-casein [7].
References [1] E. Dickinson, J. Food Eng. 22 (1994) 59. [2] D.J.M. Bergink-Martens, H.J. Bos, A. Prins, B.C. Schulte, J. Coll. Interface Sci. 138 (1990) 1. [3] D. J. M. Bergink-Martens, Ph.D. Thesis, Wageningen Agricultural University, Wageningen (1993). [4] A. Prins, F.J.G. Boerboom, H.K.A.I. Van Kabbem, Colloids and Surfaces A, Physicochem. Eng. Aspects 143 (1998) 395. [5] J. Penfold, R.M. Richardson, A. Zarbakhsh, J.R.P. Webster, D.G. Bucknall, A.R. Rennie, R.A.L. Jones, T. Cosgrove,
[6] [7]
[8]
[9]
281
R.K. Thomas, J.S. Higgins, P.D.I. Fletcher, E. Dickinson, S.J. Roser, I.A. McLure, A.R. Hillman, R.W. Richards, E.J. Staples, A.N. Burgess, E.A. Simister, J.W. White, Recent Advances in the Study of Chemical Surfaces and Interfaces by Specular Neutron Re#ection, J. Chem. Soc. Faraday Trans. 93 (1997) 3899. F.J.G. Boerboom, Netherlands Milk Dairy J. 50 (1996). R. Brinkhof, F.J.G. Boerboom, A. van Kalsbeek, H. Frederikze, J. Webster, A. A. van Well. ISIS Experimental Reports RB9247, 1998, www.isis.rl.ac.uk/ISIS98/ reports/SURF.htm. R.L. Daugherty, J.B. Franzini, E.J. Finnemore, Fluid mechanics with engineering applications, McGraw-Hill, New York, 1989. L.E. Drain, The Laser Doppler Technique, Wiley, Chichester, 1980.
Over#owing cylinder for neutron re#ection research at expanding surfaces M. Wagemaker *, F.J.G. Boerboom, H.J. Bos, A.A. van Well Interfacultair Reactor Instituut, Delft University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands Department of Food Science, University of Wageningen, The Netherlands Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands
Abstract An over#owing cylinder (OFC) suitable for neutron re#ection (NR) was designed to combine the both techniques. The two main requirements for the design are; "rstly, the expanding surface dimensions should be large enough to perform NR, secondly, the vertical dimensions should be minimized because generally there is no space for a long in#ow of the OFC (necessary to guarantee a stable-steady-state expanding liquid surface). The vertical in#ow dimensions are minimized using the design of a circular in#ow plate with a calculated perforation distribution ensuring a cylindricalsymmetric in#ow. Measurements show that the surface #ow of the designed cylinder has the required properties to study the dynamical air}liquid interface. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ha; 87.14.Ee; 79.60.Dp Keywords: Neutron re#ectometry; Over#owing cylinder technique; Protein adsorption; Expanding surface; b-casein
1. Introduction The study of the dynamic adsorption behaviour of surfactant solutions is of great interest for numerous technological processes such as foaming and emulsi"cation [1]. In understanding the stabilising properties of the adsorbed surfactant layer, there exists much interest in the dynamical properties and microscopic structure of these layers. The over#owing-cylinder (OFC) technique provides a method to study the dynamical surface behaviour of adsorbed layers in a steady state [2,3]. In this dynamical system, surface properties, such as surface tension and surface concentration, are determined as a function of the relative rate of surface expansion. The relative rate of expansion is, in case of large molecules like proteins, a measure of time scale for the unfolding of
* Corresponding author. Tel.: #31-15-278-6774; fax: #3115-278-6422. E-mail address: [email protected] (M. Wagemaker)
the adsorbed molecules, e.g., with larger expansion rates, the earlier stage of unfolding is probed [4]. In the last decade the neutron re#ection (NR) technique has been established to be a useful method for studying the depth-dependent atomic density structure in the order of nanometers [5]. The sensitivity of the neutron for hydrogen and the contrast for the neutron between hydrogen and its isotope deuterium, imply that NR o!ers an opportunity to determine the adsorbed surfactant layer structure. Many NR studies of static adsorbed layer structures have recently been performed, but these static studies are not su$cient to explain the behaviour of adsorbed layers at the non-equilibrium (or dynamical) air}water interface such as in foams and emulsions. The combination of the OFC technique and NR would relate the macroscopic quantities to the microscopic properties of the adsorbed layer, i.e. the (dynamic) structure of the layer. This combination would be a step forward in detailed understanding of the stabilising mechanism of adsorbed surfactant layers e.g. proteins. Existing over#owing cylinders are not suitable for NR experiments for two reasons. Firstly, the existing
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 0 0 1 - 3
M. Wagemaker et al. / Physica B 283 (2000) 278}281
over#owing cylinders have a relatively long vertical conical formed cylinder to ensure a laminar #ow"eld, but generally there is only limited vertical space in the experimental set-up of neutron re#ectometers. Secondly, the surface of the existing over#owing cylinders is too small to re#ect enough neutron intensity. Here we present the newly designed OFC that overcomes the two drawbacks but nevertheless ensures a cylindrical symmetric expanding surface #ow. The performance of the NR OFC will be illustrated with measurements on b-casein, a milk protein that has been subject of several studies [4,6,7].
2. Design Fig. 1 shows a cross section of the designed OFC for NR constructed of PMMA. The vertical dimension was decided to be 130 mm, and the OFC radius 90 mm (compare with 40 mm for a conventional OFC). For protein adsorption the relative surface expansion rate is inversely proportional to the time proteins have to unfold at the air}water interface. The relative expansion rate of the surface A is de"ned as [2,3]; dln A/dt"v(r)/r#dv(r)/dr,
(1)
where r is the radius and v(r) the radial velocity. To be scienti"cally interesting the cylinder should provide a range of the relative surface expansion rate, dln A/dt, large enough to probe the adsorbing mechanism at time scales in the order of 0.1 up to 10 s. To perform meaningful NR experiments the probed surface should have a homogenous structure along the re#ecting surface. Assuming that this is true for a constant relative expansion rate and given Eq. (1) the radial velocity, v(r), should be linear in the radius up to a value that allows a large enough neutron beam footprint. The #ow "eld in the central cylinder should be free of rotations and cylindrical symmetric. Because of the
limited vertical space (130 mm) the in#ow-tube is connected to the side-wall of the in#ow compartment, and thus, as can be expected, will not lead to the desired #ow characteristics in the central cylinder where the liquid rises to the expanding surface. To achieve the required #ow a circular plate was designed with a perforation density that distributes the in#ow equally around the cylinder. This can be done by either varying the perforation diameter or the distance between the perforations (perforation density). The latter method was applied for this is technically more straightforward. To calculate this distribution of mutual perforation distances, it was necessary to determine the pressure distribution in the annular region outside the perforated plate (inside the instream compartment). For reasons of simplicity, it has been assumed that the total pressure in the #ow "eld is the assembly of two components, a static pressure and a stagnation pressure. For the total pressure applies: p "ov#p
(2)
where p is the total pressure, p the static pressure, o the density and v the #ow velocity. Due to friction e!ects with the wall the total pressure will decrease with the #ow along the annulus. The loss in total pressure due to friction is, over a length ¸ with a hydraulic radius R (7.5 mm for the in#ow compartment section of 20;60 mm) and using the Poisseulle friction coe$cient for laminar #ow [8]: *p "32gR\¸v
(3)
where g is the liquid viscosity. The in#uence of the curvature of the in#ow compartment on the #ow can be neglected taken the maximum liquid velocity that will be applied. The #ow-rate through a perforation is determined by the pressure di!erence across the perforation, i.e. the di!erence between inside p and outside p of the perfor ated plate, and the drag coe$cient of the perforation, c " ("0.86 for 1 mm diameter perforations [8]): p!p "c ou, "
Fig. 1. Cross-section of the over#owing cylinder designed for neutron re#ectometry studies.
279
(4)
where p (assumed constant) is the pressure at the main cylinder side of the circular plate and u the liquid velocity through the perforation. Applying Eqs. (2)}(4) and the requirement of a constant in#ow per unit length in the #ow direction, leads to the speci"c perforation distribution that should provide a rotation free and cylindrical symmetric #ow"eld in the central cylinder. In addition to prevent rotation, radial-directed plates have been placed in the main compartment.
280
M. Wagemaker et al. / Physica B 283 (2000) 278}281
The plate designed for the presented cylinder was constructed of PVC (length 1002 mm, width 60 mm and thickness 1 mm) with 72 rows of 10 perforations 2.5 mm in diameter. The distance between the rows of perforations was calculated for one half of the plate (the #ow is symmetric left and right of the in#ow) and increased downstream starting with 5.5 mm at the in#ow up to 20.0 mm opposite of the circular placed plate. The liquid trajectory through the OFC system is as follows (Fig. 1); the liquid enters the circular in#ow compartment from where it is equally distributed, through the calculated perforation distribution, in the main cylinder. After the liquid enters the main cylinder it rises through the central cylinder and eventually #ows over the rim into the collecting cylinder. From there it is pumped back to the in#ow compartment, via a decoupled system to prevent vibrations that could disturb to the expanding liquid surface.
Fig. 2. Radial surface velocity v(r) as a function of the surface #ow radius for two concentrations b-casein, 0.3 and 1.0 g/l, for each concentration for two falling "lm lengths H , at constant #ow rate Q"40 cm/s.
3. Performance The b-casein used in the experiments was purchased from Eurial Produits Industriels and dissolved in demineralised water. The pH of the aqueous solution was stabilised at 6.7 with a 75 mmol/l Na HPO /KH PO solution. To prevent bacteria growth 0.2 g/l NaN was added. For two b-casein concentrations the wetting "lm length H was varied at a constant #ow rate Q" 40 cm/s. Note that only the values of the #ow rate and the length of the wetting "lm (H in Fig. 1) can be imposed on the liquid over#owing cylinder system. The other parameters are determined autonomously by the system [2,3]. The radial velocity v(r) of the expanding surface was measured using Laser Doppler Anemometry (LDA) [9]. The expanding surface #ow, v(r), showed to be free of rotations and cylindrical symmetric. For two b-casein concentrations the radial velocity v(r) and the relative surface expansion rate dln A/dt were measured as a function of wetting "lm length H , as shown in Figs. 2 and 3, respectively. The relative expansion rate, dln A/dt, can be directly determined out of v(r) using Eq. (1). For the OFC, the driving mechanism of the expanding surface for surfactant solutions was concluded to be the surface tension gradient generated by the free falling part of the wetting "lm [2,3]. Above a certain wetting "lm length the free falling part does not increase and is consequently not able to increase the relative expansion rate as can be seen in Fig. 3 for the newly designed OFC. Up to a certain "lm length the relative expansion rate is zero. This is assumed to be the result of a rigid b-casein "lm (held together by lateral interactions) build up on the surface and extending into the free falling part of the wetting "lm [4]. Such a "lm is able to resist the shear stress between the bulk #ow and the protein "lm and thus keeping the relative expansion rate to zero.
Fig. 3. Relative expansion rate, dln A/dt, as a function of the wetting "lm length, H , at constant #ow rate Q"40 cm/s for two concentrations b-casein, 0.3 and 1.0 g/l.
The range of dln A/dt, a measure of adsorption time window, is large enough to in#uence the properties of the adsorbing protein molecules strongly. Therefore, the newly designed cylinder o!ers a large enough range in dln A/dt to be interesting in studying the mechanical properties of adsorbing proteins such as b-casein. For NR experiments the probed surface should have a homogenous structure along the re#ecting surface. Therefore the relative expansion rate should be constant over a large enough expanding surface de"ned by the radius. For the low surfactant concentration this is not a problem, v(r) is linear in r at least up to 60 mm (conform Fig. 2 and Eq. (1)), for the high concentration in combination with a large wetting "lm length, the linear region becomes very limited. The strong non-linear behaviour at relatively small radii compared to conventional cylinders could be caused by the di!erence of the #ow properties in the central cylinder. For the conventional cylinder it was observed to be laminar (parabolic velocity pro"le) [2,3] and for the NR OFC it was observed to be more like a crop-#ow. We conclude that the designed over#owing cylinder described in this paper satis"es the demand that it generates a tuneable expanding surface properties comparable with conventional over#owing cylinders. For high concentrations surfactant one has to consider the nonlinearity of the radial velocity pro"le. First experiments with this OFC are successfully performed at the
M. Wagemaker et al. / Physica B 283 (2000) 278}281
re#ectometer SURF at ISIS in a study to the adsorption mechanism of b-casein [7].
References [1] E. Dickinson, J. Food Eng. 22 (1994) 59. [2] D.J.M. Bergink-Martens, H.J. Bos, A. Prins, B.C. Schulte, J. Coll. Interface Sci. 138 (1990) 1. [3] D. J. M. Bergink-Martens, Ph.D. Thesis, Wageningen Agricultural University, Wageningen (1993). [4] A. Prins, F.J.G. Boerboom, H.K.A.I. Van Kabbem, Colloids and Surfaces A, Physicochem. Eng. Aspects 143 (1998) 395. [5] J. Penfold, R.M. Richardson, A. Zarbakhsh, J.R.P. Webster, D.G. Bucknall, A.R. Rennie, R.A.L. Jones, T. Cosgrove,
[6] [7]
[8]
[9]
281
R.K. Thomas, J.S. Higgins, P.D.I. Fletcher, E. Dickinson, S.J. Roser, I.A. McLure, A.R. Hillman, R.W. Richards, E.J. Staples, A.N. Burgess, E.A. Simister, J.W. White, Recent Advances in the Study of Chemical Surfaces and Interfaces by Specular Neutron Re#ection, J. Chem. Soc. Faraday Trans. 93 (1997) 3899. F.J.G. Boerboom, Netherlands Milk Dairy J. 50 (1996). R. Brinkhof, F.J.G. Boerboom, A. van Kalsbeek, H. Frederikze, J. Webster, A. A. van Well. ISIS Experimental Reports RB9247, 1998, www.isis.rl.ac.uk/ISIS98/ reports/SURF.htm. R.L. Daugherty, J.B. Franzini, E.J. Finnemore, Fluid mechanics with engineering applications, McGraw-Hill, New York, 1989. L.E. Drain, The Laser Doppler Technique, Wiley, Chichester, 1980.