Modified Power Law Formula for the Characterization of Dispersions of Collagen Nanofibrils

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Modified Power Law Formula for the Characterization of Dispersions of Collagen Nanofibrils

Modified Power Law Formula for the Characterization of Dispersions of Collagen Nanofibrils

Xufang (Katie) Liu (MS, 18) Department of Chemical Engineering Manhattan College

Riverdale, New York

Abstract The United States patent, USP #6660829, pertains to the production of collagen-based products in the form of dispersions and macroporous structures using untreated raw fibrillar type I bovine corium as the starting material. The resulting dispersions have improved characteristics making them ideal for use in environmental applications as a settling aid, a filtration aid, a fractionation medium, an oil droplet stabilizer, a water purification aid, and a water siphoning aid. The dispersions may be further treated in accordance with the methods described in the patent to form macroporous structures suitable for biotechnological applications including use as a cell culturing substrate and non-biotechnological applications including use as an organic aerogel. Analysis of the admixtures produced by blending standard formulations of collagen dispersions with metal dust, inerts or metallic particles indicate that the collagen matrix may be used as a sacrificial scaffold. In this analysis, physical properties and microscopy were used to assess the quality of the dispersion. Statistical analyses were used to identify the potential for characterization using dynamic power law parameters, hysteresis, pore size, density, morphology, number and nature of crosslinks, and the possibility of connecting channels and flow-through. A modified power law formula and calculation technique is suggested for the characterization of the shear stress-shear rate description of the rheology of the collagen dispersion. Experimental data and analyses are presented.

Keywords nanofibrils, power law, shear stress, shear rate, kurtosis

  1. INTRODUCTION

    Collagen is a biodegradable polymeric fibrous protein found in all animals. In a series of steps, the collagen molecule assembles into a fiber that has the appearance of a rope. The material is insoluble in water, but can retain many times its own mass in water near its charged surface. This and the ability to unravel the fiber thus maximizing the surface area is the key physical property that leads to numerous environmental and biotechnological applications[1],[2],[3],[4],[5]. With regard to environmental applications, when added to sludge or any material with suspended solids, a collagen dispersion causes agglomeration, the formation of large flocs, and settling, all at a very rapid rate. The material has proven to be effective in the rapid agglomeration of fine solids in all types of sludge: industrial, water treatment, wastewater, inert suspensions, and kaolin.

    It has been discovered that collagen dispersions may also be used in other environmental applications such as, as an aid to

    Gennaro J. Maffia, PhD

    Department of Chemical Engineering Manhattan College

    Riverdale, New York

    filtration, separation of pollutants (including metals and soluble organic molecules) from aqueous streams, selective fractionation of molecules, and oil droplet stabilization. Moreover, because treated collagen can hold hundreds of times its mass in water, its use in water purification (with minimal energy consumption) and in water siphoning has been discovered and quantified. All of these applications are based on the affinity of the activated surface of collagen, carrying positive charges, for the negative end of the polar water molecule.

    Further processing of the dispersions yields products suitable for biotechnological applications[6],[7]. When the collagen dispersion is frozen and then freeze dried, the resulting material retains the overall dimensions of the original frozen material. However, over 99% of the volume is empty and the structure of the protein is a spongy organic aerogel with controllable pore size, good mechanical properties and a density of one thousandth of water. This solid material can be cross-linked to anchor or memorize its shape, pore size and morphology.

    Covalent bonds, between adjacent collagen molecules, are formed during crosslinking; thus the resulting material will no longer disperse or retain water. When placed in water, the cross-linked collagen sinks because the specific gravity is slightly higher than that of water. During the process of crosslinking, the material that is produced is also sterile. This material has enormous potential in biotechnology especially in the area of cell culture. Some of the cell culture applications include substrates for: a) achieving high cell density in bioreactors leading to increased productivity and reduced reactor sizes; b) hosting unusual and hard-to-culture cells that are used for a variety of applications including biosensors; c) organ and tissue technology that have medical implications (examples are organ regrowth, skin replacement, coating of prostheses and implants, etc.); d) coating of cell culture devices such as roller bottles or glass beads; e) collagen membranes for cell culture and biomolecule delivery; and f) controlled release of pharmaceuticals. In non-biotechnology applications the freeze dried, cross-linked collagen matrix can serve as an organic aerogel. Other possible uses for this material include encapsulation of a wide variety of organisms, enzymes and synthetic material.

  2. MATERIALS AND METHODS POWER LAW PARAMETER

    1. Method to Develop Collagen Nanofibrils

      1. Weighed approximately 1kg of the Raw Bovine Dermis collagen sheets

      2. Placed into ball mill with zirconia beads

      3. Filled mill with deionized water until it covered the collagen and beads

      4. Closed, sealed, and let run for approximately 2 days

      5. Collected milled collagen and placed equally into 4 centrifuge bottles

      6. Ran centrifuge at 5C for 15 minutes to separate the water from the collagen nanofibrils

      7. Top liquid was discarded and centrifuge bottles were filled with clean DI water

      8. Ran centrifuge twice more until top liquid looked clean

      9. Collagen paste was ready to use and stored in the refrigerator

    2. Method of Formulating 1% Collagen Dispersion

      1. Added acetic acid and deionized water by weight to pre-weighed amount of collagen nanofibrils produced above

      2. Blended for approximately 5 minutes or until dispersion became thicker and homogenous

      3. Stored in refrigerator for later use

    3. Method of Experimental Tests

      1. Previously made 1% and 2% collagen dispersions were taken out of refrigerator and left out for an hour

      2. These samples were analyzed by a Viscometer that collected the viscosity, shear stress, shear rate, and pressure

      3. Each day, four replicated and two treatments (increase and decrease of shear rate) were performed using Viscometer

      4. Viscosity, shear stress, shear rate and pressure data was monitored and recorded

      5. These tests ran for a total of 11 days until the shear stress became steady

      6. Data was collected and analyzed by excel

    4. Summary of the Dispersion Process

    Raw collagen from a variety of sources is the starting material in the manufacture and modification of collagen nanofibrils. The raw material has the appearance of white ground protein as shown in Fig. 1.

    Fig. 1. A collagen molecule after a series of steps assembled into the fiber tat has the appearance of rope

    It has been discovered that the above described existing collagen-based applications are enhanced, and novel applications possible, using raw fibrillar type I bovine corium as the starting material. Corium is the dermis layer of the hide and is rich in collagen-based connective tissue. While corium has been indicated as a preferred source of collagen for at least some applications, the applicant has discovered that use of a heterogeneous solution of corium as the starting material, as opposed to purified collagen derived from corium, produces superior end-products including new applications and results not heretofore observed.

    Previously, corium was pre-treated to remove fats, triglycerides, and other soluble compounds. The resulting raw collagen was then conventionally dried and milled in a knife mill. In the present invention, a dilute solution of the corium itself is milled in a ball mill containing zirconia media for one to two weeks. The pretreatment steps are avoided. Once milling is completed, the resulting material is strained, washed, and then subjected to low temperature centrifugation and the supernatant decanted. This process is repeated several times until no fats or other soluble materials appear in the upper phase and the supernatant is clear. The lower phase containing collagen is then blended in a solution containing an organic acid to form a dispersion and allowed to thicken. The resulting dispersion has improved physical properties and results in enhanced performance when used in various environmental applications.

    Fig. 2. Starting material fibers at 5 microns

    The above dispersion may be further processed to form physically improved collagen macroporous structures or substrates capable of utilization in various biotechnological applications. During the blending stage any material for encapsulation or controlled release is added.

    Fig. 3. Collagen nanofibrils before being unraveled in the ball mill

    There has thus been outlined, rather broadly, some important features of the invention in order that the detailed description thereof that follows may be better understood, and in order that the present contribution to the art may be better appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form the subject matter of the claims appended hereto. In this respect, before explaining at least one embodiment of the invention in detail, it is to be understood that the invention is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings.

    Fig. 4. Final Bovine Nanofibrils[8]

    This invention is capable of other embodiments as presented and of being practiced and carried out in various ways, biomedical and environmental. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. As such, those scientists and engineers working in protein technology will appreciate that the conception, upon which this research is based, may readily be utilized as a basis for the designing of other structures, methods and systems for carrying out the several purposes of the present invention[9],[10],[11],[12].

    Fig. 5. Atomic force microscope (AFM) micrograph of collagen nanofibrils. Note the visible d-spacing.

  3. DATA: ANALYSIS OF RESULTS

    1. ANOVA TEST F Distribution and t-Distribution

      TABLE I. DAY 2 DATA FROM 3.57% COLLAGEN PASTE

      Day 2 : Data From 3.75% Collagen Paste

      Parameter(a)

      Parameter(b)

      Directions

      Trial 1

      7.2218

      0.1978

      Increase

      4.8652

      0.2750

      decrease

      Trial 2

      5.1141

      0.2389

      increase

      5.0947

      0.2360

      decrease

      Trial 3

      5.1732

      0.2321

      increase

      5.0405

      0.2357

      decrease

      Trial 4

      5.1732

      0.2244

      increase

      5.0385

      0.2318

      decrease

      average a

      5.3401

      std. dev. a

      0.7666

      average b

      0.2340

      std. dev. b

      0.0211

      Table 1 shows the average value of parameter(a) and Parameter(b) in different treatments (increase/ decrease the shear rate) for day 2, and also the average value and standard deviation of parameter (a) and parameter (b) for all four trials.

      TABLE II. DATA ANALYSIS FROM DAY 2 RESULTS

      Day 2: t Distribution

      Testing of Means

      Observations

      Do increase first

      H0: b=0.22

      t0

      0.3666

      H1: b 0.22

      absolute(t0)

      0.3666

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.22

      Do decrease second

      H0: b=0.24

      t0

      0.4548

      H1: b 0.24

      absolute(t0)

      0.4548

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.24

      Table 2 is the t-Distribution for day 2, from the t- distrubution, one can conclde that the increase and decrease treatments dont matter for the value of parameter(b), where increase means increase the shear rate, and decrease means decrease shear rate to return to original shear rate.The purpose of the treatment is to test the hysteresis.

      Day 2: SS Analysis

      Trial

      Increase

      Decrease

      1

      0.1978

      0.2750

      2

      0.2389

      0.2360

      3

      0.2321

      0.2357

      4

      0.2244

      0.2318

      Average

      0.2233

      0.2446

      std deviation

      0.0180

      0.0203

      Observations

      Total

      0.8932

      0.9785

      1.8717

      Average

      0.2233

      0.2446

      0.2340

      0.2340

      ss treatments

      0.000910

      Trial 1

      0.000650

      0.000923

      Trial 2

      0.000243

      0.000074

      Trial 3

      0.000077

      0.000080

      Trial 4

      0.000001

      0.000164

      Total

      0.000972

      0.001241

      ss error

      0.002213

      ss total

      0.003123

      TABLE III. DAY 2 SS ANALYSIS

      ss treatments

      0.000425

      Trial 1

      0.000568

      0.000049

      Trial 2

      0.000153

      0.000000

      Trial 3

      0.000036

      0.000010

      Trial 4

      0.000030

      0.000018

      Total

      0.000786

      0.000077

      ss error

      0.000863

      ss Total

      0.001288

      Table 3 is the data analysis for One-Way ANOVA for the error and total Sum of Square for day 2.

      Day 2: ANOVA

      Between treatments

      ss

      DOF

      Mean square

      F0

      ss treatments

      0.000910

      1

      0.000910

      2.4654

      ss errors

      0.002213

      6

      0.000369

      ss Total

      0.003123

      7

      F(0.05,1,6)

      5.9874

      H0:

      Treatments( increase, decrease) don't matter

      H1:

      treatments matter

      If F0>F,

      reject H0

      fail to reject, therefore, treatments don't matter

      TABLE IV. DAY 2 DATA ANALYSIS FOR TREATMENT

      Table 7 is the data analysis for One-Way ANOVA for the error and total Sum of Squares for Day 6.

      Table 4 is the Test on Means of Normal Distribution- Variance Known Analysis for Day 2.

      Day 6: Data From 3.75% Collagen Paste

      Parameter(a)

      Parameter(b)

      Directions

      Trial 1

      7.3082

      0.2023

      increase

      5.7185

      0.2477

      decrease

      Trial 2

      5.8183

      0.2385

      increase

      5.6019

      0.2411

      decrease

      Trial 3

      5.6763

      0.2321

      increase

      5.4866

      0.2375

      decrease

      Trial 4

      5.5823

      0.2316

      increase

      5.4390

      0.2365

      decrease

      average a

      5.8289

      std. dev. a

      0.6101

      average b

      0.2334

      std. dev. b

      0.0136

      TABLE V. DAY 6 DATA FROM 3.57% COLLAGEN PASTE

      Day 6 : ANOVA

      Between treatments

      ss

      DOF

      Mean square

      F0

      ss treatments

      0.000425

      1

      0.000425

      2.9522

      ss errors

      0.000863

      6

      0.000144

      ss Total

      0.001288

      7

      F(0.05,1,6)

      5.9874

      H0:

      Treatments( increase, decrease) don't matter

      H1:

      treatments matter

      If F0>F,

      reject H0

      fail to reject, therefore, treatments don't matter

      TABLE VIII. DAY 6 DATA ANALYSIS FOR TREATMENT

      Table 8 is the Test on Means of Normal Distribution- Variance Known Analysis for Day 6.

      Day 11: Data From 3.75% Collagen Paste

      Parameter(a)

      Parameter(b)

      Directions

      Trial 1

      6.6619

      0.2036

      increase

      5.1192

      0.2569

      decrease

      Trial 2

      5.0820

      0.2530

      increase

      5.1213

      0.2466

      decrease

      Trial 3

      5.2425

      0.2434

      increase

      5.2783

      0.2391

      decrease

      Trial 4

      5.2904

      0.2355

      increase

      5.2683

      0.2376

      decrease

      average a

      5.3830

      std. dev. a

      0.5233

      average b

      0.2395

      std. dev. b

      0.0163

      TABLE IX. DAY 11 DATA FROM 3.57% COLLAGEN PASTE

      Table 5 shows the average value of parameter(a) and Parameter(b) in different treatments (increase/ decrease shear rate) for day 6, and the average value and standard deviation of parameter (a) and parameter (b) for all four trials.

      Day 6: t Distribution

      Testing of Means

      Observations

      Do increase first

      H0: b=0.23

      t0

      -0.4787

      H1: b 0.23

      absolute(t0)

      0.4787

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.23

      Do decrease second

      H0: b=0.24

      t0

      0.2763

      H1: b 0.24

      absolute(t0)

      0.2763

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.24

      TABLE VI. DATA ANALYSIS FROM DAY 6 RESULTS

      Table 6 is the t-Distribution for day 6, from the t- distrubution, one can conclde that treatments(increase and decrease shear rate) dont matter for the value of parameter(b).

      Day 6: SS Analysis

      Trial

      Increase

      Decrease

      1

      0.2023

      0.2477

      2

      0.2385

      0.2411

      3

      0.2321

      0.2375

      4

      0.2316

      0.2365

      Average

      0.2261

      0.2407

      std. dev.

      0.0162

      0.0051

      Observations

      Total

      0.9045

      0.9628

      1.8673

      Average

      0.2261

      0.2407

      0.2334

      0.2334

      TABLE VII. DAY 6 SS ANALYSIS

      Table 9 Shows the average value of parameter (a) and parameter (b) in Different treatments( increase/ decrease) for day 11, and the average value and standard deviation of parameter (a) and parameter (b) for all four trials

      DAY 11: t Distribution

      Testing of Means

      Observations

      Do increase first

      H0: b=0.23

      t0

      0.3619

      H1: b 0.23

      absolute(t0)

      0.3619

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.23

      Do decrease second

      H0: b=0.25

      t0

      -1.1216

      H1: b 0.25

      absolute(t0)

      1.1216

      t(0.05,3)

      3.1824

      If t0 >t, reject

      Fail to reject, therefore, b=0.25

      TABLE X. DATA ANALYSIS FROM DAY 11 RESULTS

      Table 10 is the t-Distribution for day 11, from the t- Distrubution, one can conclde that the increase and decrease treatments dont matter for the value of parameter(b).

      TABLE XI. DAY 11 SS ANALYSIS

      Day 11: SS Analysis

      Trial

      Increase

      Decrease

      1

      0.2036

      0.2569

      2

      0.2530

      0.2466

      3

      0.2434

      0.2391

      4

      0.2355

      0.2376

      Average

      0.2339

      0.2451

      std. dev.

      0.0214

      0.0088

      Observations

      Total

      0.9355

      0.9802

      1.9157

      Average

      0.2339

      0.2451

      0.2395

      0.2395

      ss treatments

      0.000250

      Trial 1

      0.000917

      0.000140

      Trial 2

      0.000366

      0.000002

      Trial 3

      0.000091

      0.000035

      Trial 4

      0.000003

      0.000056

      Total

      0.001376

      0.000234

      ss error

      0.001609

      ss Total

      0.001859

      TABLE XIII. AVERAGE DATA OF POWER LAW PARAMETER FOR 1% COLLAGEN DISPERSION IN 11 DAYS

      1% collagen from 3.57% paste

      Day

      average parameter( a)

      Average parameter( b)

      1

      4.97

      0.197

      2

      5.34

      0.23

      3

      5.22

      0.22

      4

      4.92

      0.23

      5

      6.53

      0.23

      6

      5.83

      0.23

      7

      5.45

      0.24

      8

      8.63

      0.18

      9

      5.68

      0.25

      10

      5.5

      0.24

      11

      5.38

      0.24

      Table 11 is the data analysis for One-Way ANOVA for the error and total Sum of Square for day 11.

      Day 11: ANOVA

      Between treatments

      ss

      DOF

      Mean square

      F0

      ss treatments

      0.000250

      1

      0.000250

      0.9311

      ss errors

      0.001609

      6

      0.000268

      ss Total

      0.001859

      7

      F(0.05,1,6)

      5.9874

      H0:

      Treatments( increase, decrease) don't matter

      H1:

      treatments matter

      If F0>F, reject H0

      fail to reject, treatment don't matter

      TABLE XII. DAY 11 DATA ANALYSIS FOR TREATMENT

      Table 13 is the average data of 1% collagen dispersion made from 3.57% collagen paste for parameter(a) and parameter(b) in 11 days.

      Analysis for Average parameter(a)

      Mean

      5.7682

      Standard Error

      0.3155

      Median

      5.4500

      Mode

      N/A

      std. dev. (Standard Deviation)

      1.0462

      Sample Variance

      1.0946

      Kurtosis

      6.3142

      Skewness

      2.3915

      Range

      3.7100

      Minimum

      4.9200

      Maximum

      8.6300

      Sum

      63.4500

      Count

      11.0000

      Confidence Level (95.0%)

      0.7029

      UL (Upper Limit)

      6.4711

      LL (Lower Limit)

      5.0653

      TABLE XIV. KURTOSIS AND SKEWNESS DATA OF PARAMETER A

      Table 12 is the Test on Means of Normal Distribution- Variance Known Analysis for Day 11.

      From F-distribution and t-distribution, all of the data failed to reject. Therefore, all of the parameter(b) value from the experiments are accepted. And all the treatments include increase and decrease rotor speed dont matter.

    2. Raw Data

      Kurtosis is a measurement of the probability distribution of a real-valued random variable. It is the fourth moment in statistics. It is a description of the shape of a probability distribution. A normal kurtosis value is +/- 3[13]. Skewness is a measurement of the asymmetry of the probability distribution of a real-valued random variable about its mean. A normal kurtosis value is +/-1[14]. Following is the Kutosis and Skewness analysis for 1% and 2% collagen dispersion of the average parameter (a) and parameter (b) value from day 1 to day 11 as seen in Tables 13 and 14.

      Table 14 is the analysis for average parameter (a), the kurtosis value of 6.3142 is greater than 3. And skewness 2.3915 is greater than 1. Both data are higher than the normal kurtosis and skewness.

      Analysis for Average parameter( b)

      Mean

      0.2261

      Standard Error

      0.0062

      Median

      0.2300

      Mode

      0.2300

      std. dev. (Standard Deviation)

      0.0205

      Sample Variance

      0.0004

      Kurtosis

      1.6685

      Skewness

      -1.4204

      Range

      0.0700

      Minimum

      0.1800

      Maximum

      0.2500

      Sum

      2.4870

      Count

      11.0000

      Confidence Level (95.0%)

      0.0138

      UL (Uppr Limit)

      0.2399

      LL (Lower Limit)

      0.2123

      TABLE XV. KURTOSIS AND SKEWNESS DATA OF PARAMETER B

      Table 15 is the analysis for average parameter (b), the kurtosis value of 1.6685 is less than 3. And skewness -1.4204 is out of the range between -1 and 1. Kurtosis value is in the range of the normal kurtosis, but skewness value is out of the normal range.

    3. Goal Seek Application for R2

    Goal seek is computed to further analyze the data to pick a power that is as close to 0.9999 as possible. In Table 16, these data shows the goal seek application for picked power law equation to reach the maximum R2 value. The shear rate and shear stress data came from the 1st trial decrease, R2 =0.9386 originally of 1% collagen dispersion made from 3.57% collagen at day 2. Following is the Power Law Equation:

    Day 6 : Applying goal seek to get R2

    Shear rate,1/s

    Shear Stress

    Shear ratek

    0.418

    5.9356

    0.9395

    0.522

    6.2640

    0.9546

    0.836

    7.0642

    0.9873

    1.045

    7.4300

    1.0032

    2.09

    8.7362

    1.0541

    4.18

    10.2410

    1.1077

    10.45

    12.0175

    1.1827

    12.51

    12.0096

    1.1980

    20.94

    13.4435

    1.2429

    41.82

    15.0134

    1.3059

    Goal seek approach

    slope

    24.7349

    intercept

    -17.3331

    R2

    0.9986

    pick power in power law equation

    0.0715

    TABLE XVII. APPLYING GOAL SEEK TO GET R2

    SS= Shear stress, Pa SR= Shear rate, 1/s

    SS= a + b SRc (1)

    a,b,c=modified power law parameter for non-Newtonian fluids[15].

    Day 2: Applying goal seek to get R2

    Shear rate,1/s

    Shear Stress, Pa

    Shear ratek

    0.418

    4.1089

    0.4648

    0.522

    4.2125

    0.5649

    0.836

    4.7401

    0.8544

    1.045

    4.9533

    1.0394

    2.09

    5.7893

    1.9108

    4.18

    6.8134

    3.5129

    10.45

    7.6076

    7.8564

    12.51

    9.2199

    9.2016

    20.94

    10.7003

    14.4672

    41.82

    17.4808

    26.5627

    Goal seek approach

    slope

    0.4854

    intercept

    4.3378

    R2

    0.9855

    pick power in power law equation

    0.8784

    TABLE XVI. APPLYING GOAL SEEK TO GET R2

    In Table 17, these data shows the goal seek application for picked power in power law equation to reach the maximum R2. shear rate and shear stress data came from 1st trial increase, R2 =0.9932 originally of 1% collagen dispersion made from 3.57% collagen at day 6.

    TABLE XVIII. APPLYING GOAL SEEK TO GET R2

    Day 11 : Applying goal seek to get R2

    Shear rate,1/s

    Shear Stress

    Shear ratek

    0.418

    5.4758

    0.9245

    0.522

    5.7420

    0.9432

    0.836

    6.4288

    0.9840

    1.045

    6.7403

    1.0040

    2.09

    7.9002

    1.0686

    4.18

    9.1124

    1.1373

    10.45

    11.0770

    1.2351

    12.51

    11.0088

    1.2552

    20.94

    12.4384

    1.3148

    41.82

    13.7588

    1.3992

    Goal seek approach

    slope

    17.6879

    intercept

    -10.9590

    R2

    0.9984

    pick power in power law equation

    0.0900

    Table 16, these data shows the goal seek application for picked power in power law equation to reach the maximum R2. shear rate and shear stress data came from 1st trial increase, R2 =0.9932 originally of 1% collagen dispersion made from 3.57% collagen at day 2.

    In Table 18, these data shows the goal seek application for picked power in power law equation to reach the maximum R2. shear rate and shear stress data came from 1st trial increase, R2 =0.9962 originally of 1% collagen dispersion made from 3.57% collagen at day 11.

  4. APPENDIX 1: POWER LAW FORMULA

    Appendix 2: Sample Power Law Analysis-Figure 6

    Fig. 6. Log data of both the shear stress as a function of shear rate.

    Appendix 3: Sample Power Law Parameters Analysis

    Day 6( 1% collagen)

    Parameter(a)

    Parameter(b)

    Directions

    Trial 1

    7.3082

    0.2023

    increase

    5.7185

    0.2477

    decrease

    Trial 2

    5.8183

    0.2385

    increase

    5.6019

    0.2411

    decrease

    Trial 3

    5.6763

    0.2321

    increase

    5.4866

    0.2375

    decrease

    Trial 4

    5.5823

    0.2316

    increase

    5.4390

    0.2365

    decrease

    average a

    5.8289

    std. dev. a

    0.6101

    average b

    0.2334

    std. dev. b

    0.0136

    At Day 6, 1% of collagen dispersion was taken out from the refrigerate and then left for an hour. Then the 1% dispersion was analyzed by viscometer. Followed by monitoring and recording Viscosity, shear stress, Shear rate and pressure data in both increasing and decreasing shear rate directions. And then excel was used to analyze the data collected.

  5. CONCLUSION

    From all the data collected, power law Intercept is not zero for log equation. After series of data analysis, ln (shear stress) vs. ln (shear rate) equation are linear with non-zero intercept. Therefore, the power law formula was then Rewrite by Taking power law until it is Close to before by using Goal seek to get R2 as close to 0.9999. In conclusion, we discovered that from day1 to day 11, it follows the Power law. As the time increased, parameter (a) kept increasing. Parameter (b) kept constant. the shear stress increased as the time increased until day 11, shear stress kept constant.

  6. ACKNOWLEDGMENT

    The authors wish to thank Eugene Bender of Collagen Matrix, Inc. for their donation of Raw Bovine Dermis sheets. The authors also wish to thank Amanda Peterman from Manhattan College for editing the paper format.

  7. REFERENCES

  1. USP 8329091 Porous Metallic Structures

  2. USP 6660829 Collagen Processing and Applications

  3. USP 4863856 Weighted Collagen Microspheres

  4. WO/2001/074929 Collagen-Based Dispersions and Macroporous Structures

  5. Nicole Aylmer, Amanda Belluccio, Gennaro J. Maffia, Effect of Collagen Nanofibrils on Turbid Water, IJERT, Vol. 7, Issue 1, January, 2018

  6. Amanda Peterman, Jane Alawi, Gennaro J. Maffia; Effect of Pore Size on the Density of Matrices Made from Collagen Nanofibrils, IJERT,

    Volume 6, Issue 8, August ,2017

  7. Control of Pore Size and Morphology in Artificial Tissue Made from Waste Corium, Gennaro Maffia, Manhattan College, Olivia Mason,

    Manhattan College, USA ICSW, March 21, 2017

  8. Use of Collagen Nanofibrils to Clarify Turbid Water, Gennaro Maffia, Manhattan College, Amanda Belluccio, Manhattan College, Nicole Aylmer, Manhattan College, USA, ICSW, March 21, 2017

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    Manhattan College, USA ICSW, March 21, 2017

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    Maffia, Gennaro

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