Name: evolution of staircase structures in diffusive convection
Uploaded: 2018-09-05T15:30:00.000+00:00
Duration: 7 min 28 s
Description: Watch this Scientific Journal Video about Evolution of Staircase Structures in Diffusive Convection at JoVE.com

This work was supported by the Chinese NSF grants (41706033, 91752108 and 41476167), Grangdong NSF grants (2017A030313242 and 2016A030311042) and LTO grant (LTOZZ1801).

1. Working Tank
Note: The experiment is carried out in a rectangular tank. The tank includes top and bottom plates and a side wall. The top and bottom plates are made of copper with electroplated surfaces. There is a water chamber within the top plate. An electric heating pad is inserted in the bottom plate. The side wall is made of transparent Plexiglas. The tank size is Lx = 257 mm (length), Ly = 65 mm (width) and Lz = 257 mm (height). The thickness of the sidewall is 9.5 mm.
<ol>
	<li>Clean the copper plates and the Plexiglas sidewall carefully with distilled water.</li>
	<li>Assemble the tank with screws to ensure that the tank is water-tight.</li>
	<li>Set up a stainless-steel supporting frame (height of 150 mm) on an optical table and fix the tank above the frame with a heat insulating slab in between, which limits the heat leakage from the working tank to the table.</li>
	<li>Insert three thermistors (temperature stability of 0.01 &#176;C) into each plate and connect them to a digital multimeter. Note these thermistors are used to monitor the temperatures of the top and bottom plates.</li>
	<li>Place a Micro-Scale Conductivity and Temperature Instrument (MSCTI) inside the tank and connect it to a Multifunction Data Acquisition (MDA). Fix the MSCTI to a Motorized Precision Translation Stage (MPTS). 
	Note: Note that the MSCTI can be moved up and down by the vertically moving, so that the temperature and salinity profiles of the working fluid are achieved. Here, the MSCTI has temperature stability of 0.01 &#176;C and salinity stability of 1%. The MPTS has positional accuracy of 0.005 mm.</li>
	<li>Set the parameters in corresponding software programs of the Digital Multimeter and the Multifunction Data Acquisition, such as sampling rates, data acquisition channels and storage paths. Here, set the sampling rates of the digital Multimeter and the Multifunction Data Acquisition as 1.0 and 128 Hz, respectively.</li>
	<li>Set the moving parameters in the software program of the MPTS, including the initial position, the lowest and highest positions, moving speed and acceleration, of the MSCTI. Here, set the moving speed and acceleration as 1 mm/s and 0.5 mm/s2, and set the lowest and highest positions as 20 and 220 mm above the bottom plate. This leads to a time period of the MPTS of 404 s for an up-down measurement. Set the initial position of the MSCTI at the lowest position.</li>
	<li>Keep the room temperature almost constant around 24 &#176;C with two high-power air conditioners (working power of 3000 W).</li>
</ol>
2. Optical Apparatus
Note: During the experiment, the evolution of the DC staircase would be monitored with the shadowgraph technique, which is fulfilled with the below procedures
<ol>
	<li>Attach a piece of tracing paper (25.7 cm x 25.7 cm) on the outside of the tank.</li>
	<li>Use a narrow beam LED lamp as the light source. Place the light source about 5 m away from the other side of the tank, so that a nearly collimated light can be generated. Note that during the experiment the DC layered fluid structure is illuminated on the tracing paper because of the density change (corresponding to the change of index of refraction) of the fluid.</li>
	<li>Place a high-speed camcorder on the same side of the tracing paper. It is about 1 m away from the tank so that the layered structures with the full-size tank can be recorded.</li>
	<li>Set the sampling rate of the camcorder. Note that the sampling rate should be proper to capture the detail of the staircase evolutions. Here, the sampling rate of the camcorder is 25 Hz.</li>
	<li>Turn on the lamp and camcorder, and slightly adjust their potions and distances, to ensure that clear images can be captured by the camcorder.</li>
</ol>
3. Working Fluid
<ol>
	<li>Prepare the saline and fresh waters in two tanks.
	<ol>
		<li>Join two identical rectangular tanks (tank A and tank B) by a flexible tube (10 cm in length, 6 mm in inner diameter and 10 mm in outer diameter) from the bottom of each one.</li>
		<li>Fill tank A with saline water, its mass concentration of salt (i.e., salinity) is 60 g/kg in this example.</li>
		<li>Fill the tank B with an equal volume of de-gassed fresh water, and use an electric magnetic stirrer to continuously homogenize the fluid.</li>
		<li>Keep the initial fluid temperature within both tanks the same as the room temperature (24 &#176;C).</li>
	</ol>
	</li>
	<li>Establish linear density stratification in the working tank.
	<ol>
		<li>Use the double-tank method29 to establish an initial linear stratification of the saline water in the working tank.</li>
		<li>Place tank A and B at the same height, which is 30 cm higher than the working tank. Join tank B and the working tank with another flexible tube (50 cm in length, 2 mm in inner diameter and 5 mm in outer diameter) from their bottoms. Due to the fluid pressure difference in these two tanks, the fluid in tank B can be slowly injected into the working tank.</li>
		<li>Control the flow speed with a peristaltic pump at 0.45 mL/s. Note the whole time of water-filling for the working tank is about 3 h. Calculate the salinity at the bottom of the working tank based on29 
		<img alt="Equation 1" src="/files/ftp_upload/58316/58316eq1.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(1) 
		where SA, V and V0 are salinity of tank A, the final fluid volume of the working tank and the initial fluid volume of tank A (or B), respectively. Using the salinity at the bottom SB and the fresh water at the top, the buoyancy frequency of initial stratification N0 is 
		<img alt="Equation 2" src="/files/ftp_upload/58316/58316eq2.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(2) 
		where g is gravitational acceleration, &#961;0 is reference density and &#946; is salinity contraction coefficient. Note the N0 is calculated as 1.14 rad/s in this example.</li>
	</ol>
	</li>
</ol>
4. Running the Experiment
<ol>
	<li>Set the boundary conditions for the working tank.
	<ol>
		<li>Connect the water chamber of the top plate to a refrigerated circulator with eight uniformly distributed plastic soft tubes (150 cm in length, 10 mm in inner diameter and 15 mm in outer diameter). Note that the temperature of the top plate depends on the temperature of the refrigerated circulator. Set the temperature of the top plate to be the same as the room temperature (24 &#176;C).</li>
		<li>Connect the electric heating pad inside the bottom plate to a Direct-Current Supply. Note a constant heat flux is provided to the working fluid during this experiment, which is calculated as 
		<img alt="Equation 3" src="/files/ftp_upload/58316/58316eq3.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(3) 
		where U, R, and A are the supplied voltage, electric resistance and effective area of the electric heating pad, respectively. In this example, the resistance and effective area are 44.12 ohm and 1.89&#215;10-2 m2. Set the supplied voltage as 60 V, so that the total heat flux Fh is 4317 W/m2.</li>
	</ol>
	</li>
	<li>Turn on the camcorder to record the flow pattern.</li>
	<li>Turn on the Digital Multimeter, Multifunction Data Acquisition to monitor the temperature of the top and bottom plates and the temperature and salinity of fluid using the MSCTI.</li>
	<li>Turn on the MPTS to move the MSCTI up and down to achieve the temperature and salinity profiles of the working fluid.</li>
	<li>Turn on the refrigerated circulator and the Direct-Current Supply to achieve the top and bottom boundary conditions of the working fluid. 
	Note: Note that the whole experiment will experience the generation, development, mergence, and disappearance of the DC staircase, and it will last about 5 hours. After the disappearance of all DC staircases, turn off the Direct-Current Supply, Refrigerated Circulator, MPTS, Digital Multimeter, Multifunction Data Acquisition, and camcorder in turn.</li>
</ol>
5. Data Processing
<ol>
	<li>Shadowgraph image
	<ol>
		<li>Use a Matlab program to convert the video recorded by the camcorder to successive images for further analysis. Tailor these images to accentuate the flow pattern within the tank. Set the digital image intensity as I(x, z), where (x, z) denotes the horizontal and vertical coordinates with the origin at the bottom-left corner of the image. Note I(x, z) varies over (0, 1) with gray level of 256. Normalize each image by a background image as30 
		<img alt="Equation 4" src="/files/ftp_upload/58316/58316eq4.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(4) 
		where <img alt="Equation 5" src="/files/ftp_upload/58316/58316eq5.jpg" /> is the average image intensity over 10 images taken before the cooling and heating being applied, <img alt="Equation 6" src="/files/ftp_upload/58316/58316eq6.jpg" /> denotes the intensity of the ith image. In this way, the stationary defects in the images can be removed. In order to examine the temporal evolution of DC pattern, each image can be converted to a single vertical intensity fluctuation profile, <img alt="Equation 7" src="/files/ftp_upload/58316/58316eq7.jpg" />, by calculating the image intensity fluctuation (i.e., root-mean-square of intensity) along the horizontal direction <img alt="Equation 7" src="/files/ftp_upload/58316/58316eq7.jpg" />. Plot the intensity fluctuation profiles <img alt="Equation 7" src="/files/ftp_upload/58316/58316eq7.jpg" /> of the successive images together with increasing time to show the evolutions of the DC staircases.</li>
	</ol>
	</li>
	<li>Temperature and salinity profiles
	<ol>
		<li>Note in this experiment the vertical profiles of temperature and salinity of the working fluid are measured by the up-down moving MSCTI. Calculate the temporal height, h(t), of the MSCTI with the mean moving speed w, time t, the starting time t0 (corresponding to the lowest position), the lowest position hL and highest position hH, as 
		<img alt="Equation 8" src="/files/ftp_upload/58316/58316eq8.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(5) 
		where <img alt="Equation 9" src="/files/ftp_upload/58316/58316eq9.jpg" /> is the MSCTI moving period from lowest (highest) to highest (lowest) position, n and &#948; are the integral and fractional parts, respectively. Then calculate the temporal height h(t) as 
		<img alt="Equation 10" src="/files/ftp_upload/58316/58316eq10.jpg" /> &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;(6) 
		Note in Equation (6), if n is even, the MSCTI is moving up; otherwise the MSCTI is moving down. Plot the time series temperature T(t) and salinity S(t) in terms of height h(t) to get the vertical temperature and salinity profiles.</li>
	</ol>
	</li>
</ol>

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The authors have nothing to disclose.

In this paper a detailed experimental protocol is described to simulate the thermohaline DC staircase structures in a rectangular tank. An initial linear density stratification of working fluid is constructed using the two-tank method. The top plate is kept at a constant temperature and the bottom one at constant heat flux. The whole evolution process of the DC staircase, including its generation, development, mergence, and disappearance, are visualized with the shadowgraph technique, and the variances of the temperature...

Double diffusive convection (DDC) is one of the most important vertical mixing processes. It occurs when the vertical density distribution of the stratified water column is controlled by two or more scalar components gradients of opposite directions, where the components have distinctly different molecular diffusivities1. It widely occurs in oceanography2, the atmosphere3, geology4, astrophysics5, material science6, metallurgy7, and architectural engineering8. DDC is present in almost half of the global ocean, and it has important effects on oceanic multi-scale processes and even climatic changes9.
There are two primary modes for DDC: salt finger (SF) and diffusive convection (DC). SF occurs when a warm, salty water mass overlies cooler, fresher water in the stratified environment. When the warm and salty water lies below the cold and fresh water, the DC will form. The remarkable feature of the DC is that the vertical profiles of temperature, salinity and density are staircase-like, composed by alternant homogenous convecting layers and thin, strongly stratified interfaces. DC mainly occurs in high latitude oceans and some interior salt lakes, such as the Arctic and Antarctic Oceans, the Okhotsk Sea, the Red Sea and African Kivu Lake10. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans11,12. It has an important effect on diapycnal mixing in the upper ocean and may significantly influence the ice-melting, which recently arouses more and more interests in the oceanography community13.
The DC staircase structure was first discovered in the Arctic Ocean in 196914. After that, Padman &#38; Dillon15, Timmermans et al.11, Sirevaag &#38; Fer16, Zhou &#38; Lu12, Guthrie et al.17, Bebieva &#38; Timmermans18, and Shibley et al.19 measured the DC staircases in different basins of the Arctic Ocean, including the vertical and horizontal scales of the convecting layer and interface, the depth and total thickness of the staircase, the vertical heat transfer, the DC processes in mesoscale eddy and the temporal and spatial changes of the staircase structures. Schmid et al.20 and Sommer et al.21 observed the DC staircases by using a microstructure profiler in Kivu Lake. They reported the main structure features and heat fluxes of DC and compared the measured heat fluxes with the existing parametric formula. With computer processing speeds improving, the numerical simulations of DC have recently been done, for example, to examine the interface structure and instability, heat transfer through interface, layer merging event, and so on22,23,24.
Field observation has greatly enhanced the understanding of ocean DC for oceanographers, but the measurement is strongly limited by indeterminate oceanic flow environments and instruments. For example, the DC interface has an extremely small vertical scale, thinner than 0.1 m in some lakes and oceans25, and some special high-resolution instruments are needed. The laboratory experiment shows its unique advantages in exploring the fundamental dynamic and thermodynamic laws of DC. With a laboratory experiment, one can observe the evolution of the DC staircase, measure the temperature and salinity, and propose some parameterizations for the oceanic applications26,27. Furthermore, in a laboratory experiment, the controlled parameters and conditions are readily adjusted as required. For example, Turner first simulated the DC staircase in the laboratory in 1965 and proposed a heat transfer parameterization across the diffusive interface, which was frequently updated and extensively used in the in situ oceanic observations28.
In this paper, a detailed experimental protocol is described to simulate the evolution process of the DC staircase, including the generation, development and disappearance, in stratified saline water heated from below. The temperature and salinity are measured by a micro-scale instrument as well as the DC staircases being monitored with the shadowgraph technique. The experimental setup, evolution process, data analysis, and discussion of results are described in detail. By altering the initial and boundary conditions, the present experimental setup and method can be used to simulate other oceanic phenomena, such as the oceanic horizontal convection, deep-sea hydrothermal eruptions, surface mixed layer deepening, the effect of submarine geothermal on ocean circulation, and so on.

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evolution of staircase structures in diffusive convection

Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different molecular diffusivities, and the larger- and smaller- diffusivity scalar gradients have negative and positive contributions for the density distribution, respectively. The DC occurs in many natural processes and engineering applications, for example, oceanography, astrophysics and metallurgy. In oceans, one of the most remarkable features of DC is that the vertical temperature and salinity profiles are staircase-like structure, composed of consecutive steps with thick homogeneous convecting layers and relatively thin and high-gradient interfaces. The DC staircases have been observed in many oceans, especially in the Arctic and Antarctic Oceans, and play an important role on the ocean circulation and climatic change. In the Arctic Ocean, there exist basin-wide and persistent DC staircases in the upper and deep oceans. The DC process has an important effect on diapycnal mixing in the upper ocean and may significantly influence the surface ice-melting. Compared to the limitations of field observations, laboratory experiment shows its unique advantage to effectively examine the dynamic and thermodynamic processes in DC, because the boundary conditions and the controlled parameters can be strictly adjusted. Here, a detailed protocol is described to simulate the evolution process of DC staircase structure, including its generation, development and disappearance, in a rectangular tank filled with stratified saline water. The experimental setup, evolution process, data analysis, and discussion of results are described in detail.

Figure 1 shows the schematic of the experimental setup. Its components are described in the protocol. The main parts are shown in Figure 1a and the detailed working tank is shown in Figure 1b. Figure 2 shows the temperature changes at the bottom (Tb, the red curve) and top (Tt, the black curve) plates. It is indicated that the temperature of the two plates are almost the same as th...

Watch this Scientific Journal Video about Evolution of Staircase Structures in Diffusive Convection at JoVE.com

Evolution of Staircase Structures in Diffusive Convection

Diffusive convection (DC) widely occurs in natural processes and engineering applications, characterized by a series of staircases with homogeneous convecting layers and stratified interfaces. An experimental procedure is described to simulate the evolution process of the DC staircase structure, including the generation, development and disappearance, in a rectangular tank.

Diffusive convection (DC) occurs when the vertical stratified density is controlled by two opposing scalar gradients that have distinctly different ...

evolution-of-staircase-structures-in-diffusive-convection

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6.4K Views.  Chinese Academy of Sciences. Diffusive convection (DC) widely occurs in natural processes and engineering applications, characterized by a series of staircases with homogeneous convecting layers and stratified interfaces. An experimental procedure is described to simulate the evolution process of the DC staircase structure, including the generation, development and disappearance, in a rectangular tank.

Video: Evolution of Staircase Structures in Diffusive Convection

Ice Generation and the Heat and Mass Transfer Phenomena of Introducing Water to a Cold Bath of Brine

We demonstrate a method for the study of the heat and mass transfer and of the freezing phenomena in a subcooled brine environment. Our experiment showed that, under the proper conditions, ice can be produced when water is introduced to a bath of cold brine. To make ice form, in addition to having the brine and water mix, the rate of heat transfer must bypass that of mass transfer. When water is introduced in the form of tiny droplets to the brine surface, the mode of heat and mass transfer is by diffusion. The buoyancy stops water from mixing with the brine underneath, but as the ice grows thicker, it slows down the rate of heat transfer, making ice more difficult to grow as a result. When water is introduced inside the brine in the form of a flow, a number of factors are found to influence how much ice can form. Brine temperature and concentration, which are the driving forces of heat and mass transfer, respectively, can affect the water-to-ice conversion ratio; lower bath temperatures and brine concentrations encourage more ice to form. The flow rheology, which can directly affect both the heat and mass transfer coefficients, is also a key factor. In addition, the flow rheology changes the area of contact of the flow with the bulk fluid.

Here, we present a protocol to demonstrate the generation of ice when water is introduced to a cold bath of brine, as a secondary refrigerant, at a range of temperatures well below the freezing point of water. It can be used as an alternative way of producing ice for industry.

We demonstrate a method for the study of the heat and mass transfer and of the freezing phenomena in a subcooled brine environment. Our experiment showed ...

Engineering

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section

The arterial network in the human vasculature comprises of ubiquitously present blood vessels with complex geometries (branches, curvatures and tortuosity). Secondary flow structures are vortical flow patterns that occur in curved arteries due to the combined action of centrifugal forces, adverse pressure gradients and inflow characteristics. Such flow morphologies are greatly affected by pulsatility and multiple harmonics of physiological inflow conditions and vary greatly in size-strength-shape characteristics compared to non-physiological (steady and oscillatory) flows 1 - 7.
Secondary flow structures may ultimately influence the wall shear stress and exposure time of blood-borne particles toward progression of atherosclerosis, restenosis, sensitization of platelets and thrombosis 4 - 6, 8 - 13. Therefore, the ability to detect and characterize these structures under laboratory-controlled conditions is precursor to further clinical investigations.
A common surgical treatment to atherosclerosis is stent implantation, to open up stenosed arteries for unobstructed blood flow. But the concomitant flow perturbations due to stent installations result in multi-scale secondary flow morphologies 4 - 6. Progressively higher order complexities such as asymmetry and loss in coherence can be induced by ensuing stent failures vis-&#224;-vis those under unperturbed flows 5. These stent failures have been classified as &#34;Types I-to-IV&#34; based on failure considerations and clinical severity 14.
This study presents a protocol for the experimental investigation of the complex secondary flow structures due to complete transverse stent fracture and linear displacement of fractured parts (&#34;Type IV&#34;) in a curved artery model. The experimental method involves the implementation of particle image velocimetry (2C-2D PIV) techniques with an archetypal carotid artery inflow waveform, a refractive index matched blood-analog working fluid for phase-averaged measurements 15 - 18. Quantitative identification of secondary flow structures was achieved using concepts of flow physics, critical point theory and a novel wavelet transform algorithm applied to experimental PIV data 5, 6, 19 - 26.

Stent implants in stenosed arterial curvatures are prone to "Type IV" failures involving the complete transverse fracture of stents and linear displacement of the fractured parts. We present a protocol for detection of secondary flow (vortical) structures in a curved artery model, downstream of clinically relevant "Type IV" stent failures.

The arterial network in the human vasculature comprises of ubiquitously present blood vessels with complex geometries (branches, curvatures and ...

Bioengineering

The Diffusion of Passive Tracers in Laminar Shear Flow

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of first injecting fluorescent dye directly into a pipe filled with distilled water and allowing it to diffuse across the cross-section of the pipe to obtain a uniformly distributed initial condition. Following this period, the laminar flow is activated with a programmable syringe pump to observe the competition of advection and diffusion of the tracer through the pipe. Asymmetries in the tracer distribution are studied and correlations between the pipe cross-section and the shape of the distribution is shown: thin channels (aspect ratio &#60;&#60; 1) produce tracers arriving with sharp fronts and tapering tails (front-loaded distributions), while thick channels (aspect ratio ~1) present the opposite behavior (back-loaded distributions). The experimental procedure is applied to capillary tubes of various geometries and is particularly relevant to microfluidic applications by dynamical similarity.

A protocol for the study of the diffusion of passive tracers in laminar pressure-driven flow is presented. The procedure is applicable to various capillary pipe geometries.

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of ...

Simulation of Early Earth Hydrothermal Chimneys in a Thermal Gradient Environment

Deep sea hydrothermal vents are self-organizing precipitates generated from geochemical disequilibria and have been proposed as a possible setting for the emergence of life. The growth of hydrothermal chimneys in a thermal gradient environment within an early Earth vent system was successfully simulated by using different hydrothermal simulants, such as sodium sulfide, which were injected into an early Earth ocean simulant containing dissolved ferrous iron. Moreover, an apparatus was developed to sufficiently cool the ocean simulant to near 0 &#176;C in a condenser vessel immersed in a cold water bath while injecting a sulfide solution at hot to room temperatures, effectively creating an artificial chimney structure in a temperature gradient environment over a period of a few hours. Such experiments with different chemistries and variable temperature&#160;gradients resulted in a variety of morphologies in the chimney structure. The use of ocean and hydrothermal fluid simulants at room temperature resulted in vertical chimneys, whereas the combination of a hot hydrothermal fluid and cold ocean simulant inhibited the formation of robust chimney structures. The customizable 3D printed condenser created for this study acts as a jacketed reaction vessel that can be easily modified and used by different researchers. It will allow the careful control of injection rate and chemical composition of vent and ocean simulants, which should help accurately simulate prebiotic reactions in chimney systems with thermal gradients similar to those of natural systems.

The goal of this protocol is to form simulated hydrothermal chimneys via chemical garden injection experiments and introduce a thermal gradient across the inorganic precipitate membrane, using a 3D printable condenser that can be reproduced for educational purposes.

Deep sea hydrothermal vents are self-organizing precipitates generated from geochemical disequilibria and have been proposed as a possible setting for the ...

Scalable Stamp Printing and Fabrication of Hemiwicking Surfaces

Hemiwicking is a process where a fluid wets a patterned surface beyond its normal wetting length due to a combination of capillary action and imbibition. This wetting phenomenon is important in many technical fields ranging from physiology to aerospace engineering. Currently, several different techniques exist for fabricating hemiwicking structures. These conventional methods, however, are often time consuming and are difficult to scale-up for large areas or are difficult to customize for specific, nonhomogeneous patterning geometries. The presented protocol provides researchers with a simple, scalable, and cost-effective method for fabricating micro-patterned hemiwicking surfaces. The method fabricates wicking structures through the use of stamp printing, polydimethylsiloxane (PDMS) molding, and thin-film surface coatings. The protocol is demonstrated for hemiwicking with ethanol on PDMS micropillar arrays coated with a 70 nm thick aluminum thin-film.

A simple protocol is provided for the fabrication of hemiwicking structures of varying sizes, shapes, and materials. The protocol uses a combination of physical stamping, PDMS molding, and thin-film surface modifications via common materials deposition techniques.

Hemiwicking is a process where a fluid wets a patterned surface beyond its normal wetting length due to a combination of capillary action and imbibition. ...

Thermocapillary Convection Space Experiment on the SJ-10 Recoverable Satellite

Thermocapillary convection is an important research subject in microgravity fluid physics. The experimental study on surface waves of thermocapillary convection in an annular liquid pool is one of the 19 scientific experimental projects on the SJ-10 recoverable satellite. Presented is a design for a payload for space experimental study on thermocapillary convection that includes the experimental model, measurement system, and control system. The specifics for the construction of an experimental model of an annular liquid pool with variable volume ratios is provided. The fluid temperatures are recorded by six thermocouples with a high sensitivity of 0.05 &#176;C at different points. The temperature distributions on the liquid free surface are captured by means of an infrared thermal camera. The free surface deformation is detected by a displacement sensor with a high accuracy of 1 &#181;m. The experimental process is fully automated. The research is focused on thermocapillary oscillation phenomena on the liquid-free surface and convective pattern transitions through analyses of experimental data and images. This research will be helpful to understand the mechanism of thermocapillary convection and will offer further insights into the nonlinear characteristics, flow instability, and bifurcation transitions of thermocapillary convection.

A protocol for the space payload design, the space experiment on thermocapillary convection, and analyses of experimental data and images are presented in this paper.

Thermocapillary convection is an important research subject in microgravity fluid physics. The experimental study on surface waves of thermocapillary ...

Preparation of Free-Surface Hyperbolic Water Vortices

Free surface vortices are present in industry in flow regulation, energy dissipation, and energy generation. Although investigated extensively, detailed experimental data regarding free surface vortices are lacking, particularly regarding the turbulence at the interface. The present paper reports on a special type of free surface vortex first proposed by Walter Schauberger in the 1960s that has an oxygen volumetric mass transfer coefficient exceeding the value of similar systems. This special type of vortex forms in a hyperbolic funnel. Different stable regimes can be stabilized with different hydraulic characteristics. Other advantages of this technology are its energy efficiency, simple design, and scalability. The flow in this hyperbolic funnel is characterized by strong turbulence and an increased surface area of the air-water interface. The local pressure strongly varies along the surface, resulting in a pronounced wavey air-water boundary layer. Due to the helical flow, these perturbations move inward, pulling the boundary layer with them. The resultant pressure gradient draws a certain air volume into the water vortex. The construction of the basic hyperbolic funnel setup and operational examples, including high-speed visualization for three different stable regimes, are presented in this work.

This paper describes how three different water vortex regimes in a hyperbolic Schauberger funnel can be created, their most important characteristics, and how associated parameters such as the oxygen transfer rates can be calculated.

Free surface vortices are present in industry in flow regulation, energy dissipation, and energy generation. Although investigated extensively, detailed ...

Flow Visualization in a Water Tunnel: Observing the Leading-edge Vortex Over a Delta Wing

Source: Jose Roberto Moreto, Gustaaf Jacobs and Xiaofeng Liu, Department of Aerospace Engineering, San Diego State University, San Diego, California
The delta wing, shown in Figure 1D, is a popular design in high-speed airplanes due to its superb performance in transonic and supersonic flight regimes. This type of wing has a small aspect ratio and high sweep angle, which reduces drag at high subsonic, transonic and supersonic flight regimes. The aspect ratio is defined as the wing span divided by the average chord <img align="middle" src="/files/ftp_upload/10459/10459eq1a.jpg" />.
An important advantage of the delta wing is its high stall angle. The stall of a delta wing is delayed compared to the stall of a high aspect ratio wing. This is because the lift of a delta wing is enhanced by the leading-edge vortex over the wing.
An effective way to observe this vortex flow phenomenon and study the vortex breakdown in a delta wing is by visualizing the flow in a water tunnel. By injecting dye in the flow surrounding a model from dye ports on the leading-edge, the vortex development and breakdown can be observed and its position measured. The data can also be used to estimate the stall angle.
<img src="/files/ftp_upload/10459/10459fig1.jpg" />
Figure 1. Typical wing planform shapes: A) Rectangular, with constant chord along span, B) elliptical, C) tapered, with variable chord along the span, and D) delta wing, an aft-swept wing with zero taper ratio.

Flow in a Water Tunnel: Leading-edge Vortex over a Delta Wing

Source: Jose Roberto Moreto, Gustaaf Jacobs and Xiaofeng Liu, Department of Aerospace Engineering, San Diego State University, San Diego, California
The ...

Education

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Aeronautical Engineering

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Considering two horizontal plates aligned along the x-axis and spaced a distance &#39;2h&#39; apart, with the y-axis perpendicular to the plates, fluid motion is assumed to be parallel. Here, the continuity equation indicates no change in velocity along the x-axis, and the Navier-Stokes equations reduce as follows:
<img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;" />
The equations in the y and z directions show no pressure gradient along these axes, indicating that pressure varies hydrostatically in the y-direction, allowing integration to yield:
<img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;" />
For parallel plates with a pressure gradient along the x-axis, the equation simplifies:
<img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;" />
By integrating twice and applying boundary conditions (u = 0 at y = +h and y = -h), we obtain:
<img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;" />
This expression reveals that the velocity profile across the gap between the plates is parabolic, with maximum velocity at y = 0, midway between the plates. The volumetric flow rate through a unit width of the plates is obtained by integrating the velocity profile across the gap.
Understanding laminar flow between parallel plates has practical applications in groundwater flow, wastewater treatment, and lubrication. For instance, this model can approximate flow in soil layers, where water moves between soil particles like flow between plates. Knowing the flow rate and velocity distribution helps engineers design efficient drainage systems and predict groundwater movement.

Stały, laminarny przepływ między równoległymi płytami

Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.
For ...

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Civil Engineering

Unit 1

Differential Analysis of Fluid Flow

KEY TERMS AND CONCEPTS

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid&#39;s steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,&#952;,z) are used to describe the radial (r), angular (&#952;), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial, meaning the velocity vector points only along the z-axis and varies solely with the radial distance r from the center of the tube.
The governing equations for fluid motion, the Navier-Stokes equations, simplify under these conditions. Without angular or radial velocity components, the axial velocity vz(r) emerges as a function of r alone. Solving the reduced Navier-Stokes equations yields a parabolic velocity profile:
<img alt="Equation 1" src="/files/ftp_upload/18065/18065_Equation 1.svg" style="text-align: center; height: 27px;" />
This profile demonstrates that viscous drag decreases the fluid velocity from the maximum at the center to zero at the tube wall. This zero velocity at the boundary, known as the no-slip condition, results from the friction between the fluid and the tube wall. Consequently, the flow is laminar, with fluid particles moving in parallel layers without lateral mixing.
Integrating the velocity profile over the cross-sectional area of the tube yields the volumetric flow rate Q, known as Poiseuille&#39;s law:
<img alt="Equation 2" src="/files/ftp_upload/18065/18065_Equation 2.svg" style="text-align: center; height: 27px;" />
Where &#916;P is the pressure difference across the length L &#160;of the tube, and &#956; is the fluid&#39;s dynamic viscosity. This relation shows that Q is highly sensitive to the tube&#39;s radius, increasing with the fourth power of R. It follows that even a slight increase in radius significantly boosts the flow rate, a principle critical in fluid transport applications.
From Poiseuille&#39;s law, the mean velocity V of the fluid can be expressed as:
<img alt="Equation 3" src="/files/ftp_upload/18065/18065_Equation 3.svg" style="text-align: center; height: 27px;" />
This average velocity is precisely half of the maximum velocity at the tube&#39;s center, confirming the parabolic velocity distribution and demonstrating the predictable, layered nature of laminar flow in a cylindrical tube.

Stały, laminarny przepływ w okrągłych rurach

Consider steady, incompressible flow through a straight cylindrical tube of constant radius R, known as Hagen&#8211;Poiseuille flow.
The cylindrical ...