ADHESIVE STRESS BETWEEN MUSHY STRUCTURE OF AQUEOUS SOLUTION AND SOLID SURFACE

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1 ISTP-16, 25, PRAGUE 16 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA ADHESIVE STRESS BETWEEN MUSHY STRUCTURE OF AQUEOUS SOLUTION AND SOLID SURFACE Masaaki Ishikawa*, Takeshi Aoyama**, Tetsuo Hirata* *Dept. of Mech. Sys., Shinshu Univ. **Grad. School of Shinshu Univ. Corresponding author: Keywords: Aqueous, Mushy structure, Adhesive stress, Adhesive energy Abstract Adhesive phenomena between mushy structure of aqueous solution and solid cold surfaces is important in fields of air-conditioning, refrigeration, food processing, chemicals, materials, constructions, sports and leisure industries. Adhesive stress between pure ice and solid surfaces is already reported [1][2][3]. According to these reports, the actual values eist in a certain range and are not unique even under the same macroscopic thermal conditions. Furthermore, adhesive phenomena of aqueous solution is not known. The adhesive stress of mushy structure of aqueous solution on a solid surface is generally small compared with the value of pure ice. According to our previous study, however, the maimum value is about twice as large as the smallest value, even under the same macroscopic thermal conditions. Furthermore, we have concluded that the deviation of the values does not depend on probability but depends on microscopic phenomena. The objective of this paper is to know an essential parameters both eperimentally and analytically which determine adhesive stresses. Copper and PVC are used as cold surface materials. Ethanol-water aqueous solution with the concentration of less than 2wt% is used. The force applied on mushy structure is measured continuously. The maimum value of the force that appears just before the removal process starts is defined as an adhesive shear force. Some important parameters that determine adhesive phenomena are derived from analysis. The main findings and results are; (1) Microscopic mushy structure depends not only on conditions of aqueous solution but on materials of cold surfaces. (2)Although surface conditions of cold surfaces are important, adhesive shear stress depends not on average surface roughness but on other surface characteristics. (3)Area epansion ratio, solid ice contact area fraction and other suitable functions that epress surface characteristics are important for adhesive shear stress as well as elasticity of mushy structure. 1 Introduction When aqueous solution is cooled at the temperature between its eutectic point and degree, mushy structure is observed as a solid phase. Mushy structure contains a lot of small ice crystals of 1s to 1s µm. Among each ice crystal eists liquid phase of an aqueous solution. Adhesion between mushy structure and a solid surface is seen in air conditioning, refrigeration, food industry, chemical industry, material processing, construction and structure, sports and leisure industry. It is useful to know adhesion between mushy structure and a solid surface. Some studies on adhesive shear stress between pure ice and a solid surface have been found. The data shown in the studies are arranged with macroscopic parameters such as temperature. It is often reported that the deviation of the eperimental data is lead by eperimental errors or microscopic effects. Although other reports refer to surface 1

2 Masaaki Ishikawa, Takeshi Aoyama, Tetsuo Hirata roughness [2][3] and to adhesive work between liquid droplets and solid surfaces [1][3], the effects are not well known so far. No studies have been found on aqueous solution. Authors have reported [6][7] estimations of elasticity of mushy structure and adhesive shear stress by modeling mechanical removal processes of mushy structure from a solid surface. Authors also have studied [4][5] adhesive shear stress measurement and discussed the effects of macroscopic factors on adhesive stress. We confirmed in the studies that mushy structure of aqueous solution shows the same tendency as pure ice shows. The adhesive shear stress is not well arranged with macroscopic factors such as temperature and concentration. Both in pure ice and aqueous solution, there are essential microscopic factors that determine adhesive shear stress. In previous studies on mushy structure of aqueous solution, concentration and subcool degree have significant effects on dendritic structure. According to the present observation, however, materials of cold surfaces also affect dendritic structure. An analytical model is also proposed to specify important parameters that affect adhesive shear stresses. 2 What is Known So Far Parameters are divided into two groups, one is related to aqueous solution and the other is related to cold surfaces. Macroscopic parameters and their effects on adhesive shear stresses are as follows. [A]Aqueous solution (1)Elapsed time from initial solidification Adhesive shear stresses are large when elapsed time is large. The elapsed time that leads to steady state is already discussed. (2)Concentration of aqueous solution It affects dendritic structure of steady state. It also affects adhesive shear stresses significantly. When concentration of aqueous solution is high, the adhesive shear stress is small. (3)Subcool degree It affects ice crystal growth rate under nonequilibrium condition. It has little effect on dendritic structure of steady state. There is no significant relation between subcool degree and adhesive shear stress. [B]Cold surface (1)Surface temperature In ref.[2], adhesive shear stress between a solid surface and pure ice is large when surface temperature is low. However, authors did not find the relation in terms of aqueous solution [4][5]. Within the present eperimental conditions, there is no significant relation between adhesive shear stress and surface temperature. (2)Heat flu No studies on the effects of heat flu on adhesive shear stress are found. Heat flu is a quantity that is related to crystal growth rate and does not strongly affect adhesive shear stress of steady state. (3)Shape and dimension of a cold surface Because mushy structure is soft, there is a possibility that it collapses during detaching process. When its concentration is low, however, mushy structure is as hard as pure ice and does not collapse. Even when shapes and dimensions of cold surfaces are different, the adhesive shear stresses vary in a certain range. It means that adhesive force is characterized by adhesive stress. (4)Surface materials To epress the characteristics of materials, the adhesive work is calculated by measuring contact angles of liquid droplets and solid surfaces. In Section 4.1, the effects of adhesive works on adhesive shear stresses are discussed. Although there is a positive correlation among them, there still is a large deviation in the data. It means that there are some other factors that affect adhesive shear stresses. According to the discussion so far, it is clear that adhesive shear stresses are not well arranged only by macroscopic conditions. Followings are the microscopic factors that affect adhesive shear stresses. [A]Aqueous solution (1)Direction of ice crystals Because it is difficult to control directions of ice crystals during mushy structure grows, the effects is not yet discussed. (2)Contact area fraction of ice and surface 2

3 ADHESIVE STRESS BETWEEN MUSHY STRUCTURE OF AQUEOUS SOLUTION AND SOLID SURFACE As shown in Fig.1, both pure ice and remained liquid phase eist on a cold surface. The area fraction of pure ice to the whole area is defined as contact area fraction. Although quantitative measurement of contact area fraction is difficult, contacting conditions are observed in Section 4.3. (3)Dimensions of ice crystals Observed in this study. (4)Single crystal and multi-crystals Even contact area fraction is equal, there is a difference of adhesive shear stress between single ice crystal and multi-crystals. However, these effects are not discussed in this study. [B]Cold surface (1)Surface condition Surface conditions such as surface roughness are important in the theory of adhesion and friction. In the case of adhesion between mushy structure and solid surfaces, surface conditions affect adhesive shear stresses. It is discussed in Section 4.2. Primaryarm ofcrystals(solid part) Higher-orderarms(solid part) Cold surface Fig.1(a) Schematic model on solid surface Liquidpart (Water or solution) Water/ice Non-equilibrium stage Relaation stage Equilibriumstage Adhesion area Solution Remanent liquid Fig.1(b) Schematic model on solid surface; back side 3 Eperiments 3.1 Adhesive Shear Stress Fig.2 shows the main part of the eperimental apparatus. The test section is located in a low temperature room. A stainless steel rectangular cylinder of 1mm thickness is located on a horizontal cold surface. Aqueous solution is poured into the cylinder and is cooled from the bottom. After 18 minutes from when mushy structure starts growing, an actuator is driven and shear remove the mushy structure and the cylinder at the same time. On the edge of the actuator is a strain gauge that detects force changes. Eperimental conditions are shown in Table 1. Ethanol-water solution of concentration of %,.1%,.3%,.5% and 2.% are used as provided aqueous solution. Copper and PVC are used as cold surfaces. Because it is known that the temperature of cold surface does not affect adhesive shear stress significantly, the temperature difference between cold surface temperature and equilibrium fusion temperature of the aqueous solution is set at 9-11K. Fig.3 shows an eample of detected force changes. When an actuator contacts the stainless cylinder, the detected force becomes large. After the force shows its maimum value, it decreases. Adhesive force is defined as the maimum value. Table 1 Eperimental conditions Aqueous solution ethanol-water Material of cold surfaces Cu, PVC Difference between T f -T w 9-11 K Concentration, wt%,.1,.3,.5, 2. Shapes and dimensions Cu, rectangular 5mm5mm 3mm3mm Cu, circle d=34mm PVC, rectangular 3mm3mm Elapsed time 18 minutes 3

4 Masaaki Ishikawa, Takeshi Aoyama, Tetsuo Hirata Actuator 1mm 4mm Mushy Structure Strain Gauge ColdSurface Fig.2 Eperimental apparatus 1 Contact Stainless-steel Cylinder AdhesionForce Thermocouples Grease Detach ElapsedTime, s Fig.3 Eample of detected force changes.3%, Cu, rectangular, 33, 11.4K Brine 72mm DigitalCamera Samplesolution Fig.4 Eperimental apparatus 2 Table 2 Eperimental conditions Material of cold surfaces Difference between T f -T w Brine Remove 3mm 22mm Cold Surface Cu, PVC 9-11 K 3.2 Observation Fig.4 shows the eperimental apparatus for observation. A transparent cold surface is located horizontally. After mushy structure growth becomes steady state, photos are taken from the bottom of the test section. Eperimental conditions are shown in Table 2. Kind of aqueous solution and its concentration are the same as that of Table 1. A glass and a transparent PVC plate are used as a solid cold surface. The difference of surface temperature and the equilibrium fusion temperature is set at 8-1K. 4 Eperimental Results and Discussion 4.1 Surface Materials and Adhesive Work Fig.5 shows the relation between concentration and adhesive shear stress. When concentration is large, the adhesive shear stress is small. Copper plates show smaller adhesive shear stress than PVCs show. However, copper plates show larger adhesive stress than PVCs show when concentration is larger than 2% [4][5]. Because heat conduction of PVC is small, dendritic ice crystals grow toward the liquid part rather than growing along on the cold surface. When concentration s large, spaces among each ice crystal are large, and contact area fraction of PVC is smaller than that of copper. Adhesive shear stress is affected mainly by contact area fraction. On the other hand, when concentration is small, spaces among each ice crystal are small, and contact area fraction is large. It means that adhesive shear stress is affected mainly by adhesive work between ice crystals and surface materials. Because PVC is an organic polymer, there is hydrogen bonding between surface material molecules and H 2 O molecules. Adhesive shear stress of PVC is then larger than that of copper. Fig.6 shows the relation between adhesive work and adhesive shear stress. Although Fig.6 shows the same tendency as ref.[1] and [3] show, the deviation of the present data is large. The adhesive shear stress is not well arranged by adhesive work. 4

5 ADHESIVE STRESS BETWEEN MUSHY STRUCTURE OF AQUEOUS SOLUTION AND SOLID SURFACE surface roughness as previous studies [2][3] show. Average surface roughness means the average mountain height, and does not contain the effects of mountain pitches. Area epansion ratio and average slope are epected parameters. Fig.8 also indicates that adhesive shear stress differs by two times among different surfaces. Concentration, wt% Fig.5 Concentration and adhesive shear stress Rectangular, 33, 9-11K Error bars refer to average +- S.D. Fig.7(a) Observed surface, copper Ra=.69µm Adhesionwork, mj/m 2 Fig.6 Adhesive work and adhesive shear stress Fig.7 shows the observed solid surfaces by AFM. The copper plate and the PVC plate used in the present eperiment show different average surface roughness by one digit. Undulation of the whole surface is also different. Because these microscopic factors affect adhesive shear stress, it is not well arranged only by macroscopic factors such as adhesive work. 4.2 Surface Roughness Eight kinds of copper plates are eamined in this section. Each surface is finished by different emery papers. Fig.8 shows the relation between average surface roughness and adhesive shear stress. It shows that adhesive shear stress is not arranged only by average Fig.7(b) Observed surface, PVC Ra=.414µm AverageSurfaceRoughness, µm Fig.8 average surface roughness and adhesive shear stress.1%, Cu, 33, 9-11K Error bars refer to average +- S.D. 5

6 Masaaki Ishikawa, Takeshi Aoyama, Tetsuo Hirata 4.3 Observation Fig.9 and Fig.1 show the observed results obtained by the eperimental apparatus shown in Fig.4. Fig.9 shows the cases of glasses, while Fig.1 shows the cases of PVCs. Because the volume fraction of mushy phase is given by an equilibrium diagram and lever law, dendritic structure is also considered to be given only by conditions of aqueous solution. However, Fig.9 and Fig.1 show different ice crystals on the cold surfaces. It means that ice crystal growth along on cold surfaces is affected by surface characteristics such as adhesive work and microscopic surface roughness. Even under the same macroscopic conditions, the contact area fractions are different among each surface material. However, it is difficult to measure contact area fraction. Fig.1 Observed ice crystals on PVC 8-1K 5 Theoretical Approach Schematic models of removing processes of mushy structure is shown in Fig.11. The first stage before detaching is called elastic deformation. The elastic energy is then released and converted to adhesive work. The elastic energy charged during the first stage is R Fd (1) When the value of eq.(1) equals to the adhesive work between mushy structure and solid surface, the whole region detaches from the solid surface. Fig.9 Observed ice crystals on glass 8-1K R Fd = γ A = γwl (2) Here γ and A is an apparent value of adhesive work and contact area, respectively. 6

7 ADHESIVE STRESS BETWEEN MUSHY STRUCTURE OF AQUEOUS SOLUTION AND SOLID SURFACE Compression stress is epressed as Apparent strain is epressed as Then we obtain σ = Eε (3) ε = (4) E σ = E (5) When eq.(5) is multiplied by WH, we obtain E F = σ WH = EWH (6) By substituting eq.(6) into eq.(1), which equals to eq.(2), we obtain 1 2 EWH 2 R E E = γwl The maimum value of eq.(6) is F = EWH (7) R ma (8) E By substituting eq.(7) into eq.(8), we obtain F = 2γWL / (9) ma By dividing both sides of eq.(9) by A, we obtain measured adhesive shear stress as R R γ τ = ma 2 (2) In terms of elastic deformation, we obtain k R = (31) E where k is a constant value that depends on macroscopic conditions. When pure adhesive work between ice crystals in mushy structure and a solid surface is epressed as γ shown in Fig.12, and apparent adhesive work that contains liquid part is epressed as γ, we obtain γ = γ (42) c 1 c2 c3 where c 1 is contact area fraction, c 2 is area epansion ratio, and c 3 is a suitable function that epresses surface characteristics. c 1 and c 2 is epressed as follows. Then we obtain Areal Areal c1 = = (53) A WL Asr Asr c2 = = (64) A WL γ τ ma = 2 c1c2c3 (75) k where γ and k are constants that are given according to macroscopic conditions. c 1 does not differ more than twice under the same macroscopic conditions. c 2 is an order of.1%. However, c 3 and elasticity E differs more than twice according to microscopic differences. Elasticity of mushy structure depends on whole dendritic structure [6][7]. It is concluded then that the main factors that produces the difference in Fig.8 are c 3 and E. Elastic deform region F = R E E W Fig.11(a) Elastic deformation process L H 7

8 Masaaki Ishikawa, Takeshi Aoyama, Tetsuo Hirata F = R E Detach W H E L Fig.11(b) Energy release and detaching process F ma Detach = R Fig.11(c) Detected force Orderof 1-1mm Liquid part (1)Suitable function c 3 in eq.(12) should be found. (2)Contact area fraction c 1 in eq.(12) should be measured. (3)Elasticity of mushy structure should be known by grabbing dendritic structure quantitatively. References [1] M. Yoshida, T. Ohichi, K. Konno and M. Gocho, Cold Region Technology Conference '91, pp , 1991 (in Japanese). [2] Y.Kamata, Y.Mizuno, K.Horiguchi and M.Yoshida, 5th Int. Symp. On Thermal Engeneering and Science for Cold Regions, pp , [3] C. Laforte, J.L. Laforte and J.C. Carriere, The Tenth International Workshop on Atmospheric Icing of Structures, s9-1, 22. [4] M. Ishikawa, T. Aoyama and T. Hirata, 14th Int. Conf. on Properties of Water and Steam, in press, 24. [5] M. Ishikawa, T. Aoyama and T. Hirata, 15th Int. Symp. on Transport Phenomena, CDROM, 24. [6] M. Ishikawa, T. Hirata and T. Fujii, Int. J. Refrigeration, 25, 2, pp , 22. [7] M. Ishikawa, T. Hirata, T. Fujii, Canadian Society of Mechanical Engineering Forum 22, CDROM, 22. Pureicecrystals γ A=WL Fig.12 Apparent and real adhesive work γ 6 Conclusions (1)When cold surface materials change, not only pure adhesive work but also dendritic structure change. Thus the adhesive shear stress is not arranged only by macroscopic factors such as adhesive work. (2)Adhesive shear stress is not arranged only by average surface roughness. Some suitable functions that represent surface characteristics are needed. (3)Elasticity of mushy structure is also an important factor to know adhesive shear stress. Future problems are as follows. 8