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1 INTEGUMENTARY PERFECTIONS Report Concerning Engineering Moisturizing Skin Lotions Authors: Miguel Bagajewicz, Season Hill, Amanda Robben, Heyde Lopez, Monica Sanders, Erin Sposato, Curtis Baade and Shamara Manora University of Oklahoma School of Chemical, Biological and Materials Engineering Norman, OK May 6, 2007

2 TABLE OF CONTENTS 1.0 Abstract Introduction Skin Properties and Disorders Humidifying Lotions Lotion Manufacturing Procedure Consumer Preference Model Thickness Adhesion Spreadability Effectiveness Absorption Rate Smoothness Greasiness Maximizing Consumer Satisfaction Competitor s Product Preference Business Model Competitor s Response Risk Analysis Conclusions Acknowledgements Works Cited

3 1.0 ABSTRACT In this paper, we apply a recently proposed methodology for product design to the case of engineering skin lotions. A consumer satisfaction model is constructed and used to engineer the lotion that maximizes consumer satisfaction. Such a formulation turns out not to be the most profitable formulation. Thus, a pricing model is used to find a formulation that maximizes profit. 2.0 INTRODUCTION Moisturizing lotions are intended to restore the skin s ability to retain water. This is primarily accomplished by adding and keeping water in the skin while restoring the lipid bilayer. Lotions for patients having some skin disorders, like ichthyosis vulgaris, which is a genetic disorder that causes dry, thickened skin, require lotions that contain desquamation agents. That is, compounds that will help shed dead skin cells through various enzymatic reactions. In addition to its main intended therapeutic purpose, one needs to pay attention to several other functionalities: lotions need to absorb quickly, the greasiness stemming from insoluble organics needs to ameliorated, etc. In addition they need to be easy to apply and make the consumer comfortable so their thickness and smoothness, among other properties like fragrance and color, need to be controlled. The main ingredients of a lotion are: active ingredients (humectants, exfoliants to promote desquamation, occlusives to prevent loss of water and emollients to fill intercellular spaces) as well as inactive ingredients such as solvents, thickeners, preservatives, buffers and fragrance among others. Among the compounds that can be used for each one of these functionalities there are some that are more effective (and usually more expensive) than others. Thus, as it often happens in products, a balance between quality and cost needs to be made. This is usually accomplished by using less expensive ingredients. To our knowledge this is a trial and error process that takes place in different companies through a variety of mostly unclassified mechanisms. The literature on product design and specifically on lotion design has been focusing on cosmetic science, relating lotion properties, such as thickness, smoothness and effectiveness, to physical properties that can be related to the ingredients used. None of these proposed procedures directly - 2 -

4 addresses the response of the consumer to quality and price simultaneously. Although pricing theory is a well-known field where such behavioral models can be found, this theory considers existing products and does not propose methods to manipulate the product structure/composition. Such connection between pricing models and product quality manipulation was recently proposed by Bagajewicz (2007). In his paper, in addition to reviewing several product design approaches, Bagajewicz discusses the need to use some elements of hedonic theory in conjunction with consumer satisfaction models to determine the most profitable product, which not always happens to be the best product from the consumer preference point of view, as anticipated above. In this paper, we apply the methodology proposed by Bagajewicz (2007), which first calls for constructing consumer preference models and use them to obtain the value of hedonic parameter in a pricing model. The pricing model is used to determine, simultaneously, the optimum price and the product composition (he used an insect repellent example). We first present some background on skin structure and disorders. Then we discuss the consumer preference model and determine the composition of a lotion that maximizes consumer preference, regardless of price. Then we present the maximum profit model and determine the corresponding lotion. 2.1 SKIN PROPERTIES AND DISORDERS The skin is the largest organ of the body, with a surface area of approximately 1.75 m 2 in the average adult. 1 The skin weighs between kg, comprising about 7% of body s total weight. It is composed of three different layers: the epidermis, dermis, and subcutaneous layers. The epidermis, the outer-most layer, is where most of the moisturizing effects take place. Figure 1 shows the layers of the epidermis. SC Stratum Lucidum Stratum Granulosum Stratum Spinosum Stratum Basale Basale Membrane Figure 1. The Layers of the Epidermis

5 The stratum corneum (SC) is the outer-most layer of the epidermis and is the part of the skin that is in direct contact with the environment. It is composed of approximately 20 layers of dead skin cells. 3 The water content in this layer is around 30%, which is important for keeping the desquamation process active and the skin an effective barrier against infection (Rawlings and Harding, 2004). The desquamation process, which occurs in the SC, sheds one layer of skin per day. Moreover, the natural moisturizing factors (NMF) also are located in the SC, which are responsible for the absorption and retention of water. In order to retain water, a hydrophobic lipid bilayer surrounds hydrophilic cells (keratinocytes) 11 where water is retained (Marino, 2001). When the skin hydration falls below 10%, the skin becomes rough, dry, and develops a fine scale (Melton, 1996). The main cause of dry skin (known as xerosis) is dehydration of the SC. Dehydration can also be caused by overexposure to water, harsh soaps or irritants, and the environment (e.g. cold, dry air). Ichthyosis is a family of genetically inherited disorders characterized by severely scaly, thickened skin. Due to a lack of water-binding components in the epidermis, the skin shows low levels of hydration and the desquamation process slows down. This genetic defect leads to a buildup of dead skin cells within the SC, producing dry scales on the skin as illustrated in Figure 2. Given that ichthyosis is a genetic disorder, it has no cure; therefore, its treatment centers on managing its signs and symptoms. Figure 2. Picture of Dry, Scaly Skin. (Geneva Foundation, 2005) - 4 -

6 The most common form of ichthyosis is ichthyosis vulgaris. It accounts for 95% of all ichthyosis cases. Numerically, one in every 250 people in the US has ichthyosis vulgaris (DiGiovanna and Robinson-Boston, 2003). Furthermore, low water content in the SC inhibits proteases for several enzymatic processes, like the desquamation process. With desquamation inhibited, the skin becomes thickened and dry. Reflection of light off of theses dried squamous cells on the surface of the skin gives the appearance of scaly skin. With ichthyosis vulgaris, the lower extremities (i.e. lower legs) are the most targeted regions of the body. Areas such as the face and folds of the body tend to be more hydrated; thus, these areas do not appear as scaly. Symptomatic treatment of ichthyosis vulgaris involves using moisturizing lotions to restore the lipid bilayer, deliver moisturizing agents to the skin, and promote desquamation. Moisturizers treat dry skin in different capacities. One method involves trapping water in the skin, by hydrating the SC and then sealing the SC to prevent transepidermal water loss water loss to the environment by diffusion. To promote desquamation and increase water binding activities, keratolytic agents, such as lactic acid, glycolic acid, salicylic acid, urea, and propylene glycol are used (DiGiovanna and Robinson-Boston, 2003). 2.2 HUMIDIFYING LOTIONS There are different types of ingredients used in lotions, each ingredient adding a specific attribute to the lotion. Primarily, lotion ingredients can be classified as active ingredients and inactive ingredients. The active ingredients help treat the skin disorders aforementioned by restoring the lipid bilayer, delivering the moisturizing agents to the SC, and promoting desquamation. Table 1 lists the different types of active ingredients and their purpose. Table 1. Active Ingredients of Lotions Classification Humectants Occlusives Exfoliants Emollients Function Attract and bind to water Prevent loss of water from skin Promote dead skin removal Fill intercellular spaces on surface of skin - 5 -

7 The active ingredients help treat the symptoms associated with xerosis and ichthyosis vulgaris. Humectants increase the moisture content of the skin by bringing water from the atmosphere into the SC. Occlusives are employed to prevent transepidermal water loss by sealing the SC. Desquamation is enhanced with the use of exfoliants, and the lipid bilayer is restored with emollients. On the other hand, the inactive ingredients make it possible for consumers to use the active ingredients. The inactive ingredients are described in Table 2. Table 2. Inactive Ingredients of Lotions Classification Solvent Emulsifier Preservatives Thickeners Buffer Fragrance Function Contains and Disperses Ingredients Helps Mix Aqueous and Oil Phases Prevent contamination by microbial organisms Increase viscosity Adjust ph of moisturizer Provide desirable scent The inactive ingredients help make the lotion more attractive for consumers to use and help deliver the active ingredients into the SC. The solvent is the primary ingredient that helps disperse the active ingredients into the SC. The lotion is comprised of aqueous and oil phases. Since water and oils do not mix well, emulsifying agents help these two phases combine more readily. Preservatives prevent fungal and microbial organisms from growing in the lotion. The thickeners, buffer and fragrance makes the product more attractive to consumers by adding the aforementioned properties listed in Table 2. From these categorizations of the active and inactive ingredients, specific chemicals and oils were examined that are known to help with the symptoms of ichthyosis vulgaris. The following tables show the ingredients considered in this paper

8 Table 3. Active Ingredients Humectants Occlusive Emollients Exfoliants Glycerin (glycerol) Mineral Oil Sunflower Oil Urea Allantoin Petrolatum Almond Sweet Oil Lactic Acid PEG Ceramide Macadamia Nut Oil Malic acid Sodium PCA (50%) Beeswax NF Hazelnut, Oil Dimethicone Coconut Oil (76%) Cholesterol Lanolin Aloe Vera Oil Grapeseed Oil Acrylates/c10-30 Alkyl Acrylate Crosspolymer Isopropyl Palmitate Decyl Oleate Palm Oil Castor Oil Table 4. Inactive Ingredients Solvent Thickeners Preservatives Buffer Emulsifier SC Lipid Color Fragrance Deionized Water Sorbitol Rice Bran Oil Citric Acid Sorbitan Monolaurate γ-linoleic Acid TiO 2 Hazelnut Fragrance Glyceryl Stearate Disodium EDTA TEA Cetearyl Alcohol Oleic Acid Potassium Sorbate NaOH Cetyl Alcohol Stearic Acid Vitamin C (L-Ascorbic Acid) Maleic Acid Xanthan Gum Phenoxyethanol Carbomer Methylparaben Isostearic Acid Propylparaben According to the Food & Drug Administration (FDA), a cosmetic is defined as, articles intended to be applied to the human body for cleansing, beautifying, promoting attractiveness. (Food, Drug, and Cosmetic Act, Sec. 201(i), 2004). Skin moisturizers are considered cosmetic products as long as the concentration of ingredients stays below the Cosmetic Ingredient Review (CIR) allowed maximums, removing any jurisdiction of the FDA for the ingredients used. Each individual ingredient was checked to see if it had a concentration constraint in place from the CIR. Table 5 shows some of the restrictions used to determine the lotion formulation

9 Table 5. Concentration Boundary for EachType of Ingredient Type of Ingredient Min Concentration Max Concentration Solvent 65.00% 75.00% SC-Lipid 5.00% 35.00% Emulsifiers 1.00% 20.00% Humectants 0.05% 15.00% Emollients 0.05% 15.00% Preservatives 0.10% 10.00% Fragrance 0.00% 0.25% Occlusive 0.10% 10.00% Thickener 0.10% 2.00% Buffer 0.00% 0.00% Exfoliants 0.10% 1.00% Other ingredients had more specifications as to what other chemicals can be used with the ingredient. These restrictions were adhered to as well. The lotion has to be reviewed by the CIR before it can be introduced to the market. There is no cost to have the lotion product reviewed by the CIR Board, where the concentration of all the ingredients is checked. 3.0 LOTION MANUFACTURING PROCEDURE The actual manufacturing procedure consists of mixing the oil and water phases together. The following steps show how the lotion is made. 1. Heat and mix the aqueous and oil phases separately 2. Combine both phases into one batch 3. Perform post treatment modifications (i.e. decrease particle size) A bath sonicator is used to decrease the particle size. This works by using vibrations to break apart larger particles and mix them throughout the emulsion. A colloid mill and homogenizer are also used to further decrease the particle size. The equipment costs are outlined in Table 6. The prices came from various vendors from around the U.S

10 Table 6. Equipment Costs and Specifications Equipment Cost ($) Bath Sonicator $60,000 Tanks: Storage $10,000 Water phase (Batch Tank) $8,000 Oil phase (Batch Tank) $4,000 Colloid Mill $25,000 Homogenizer $11,000 PD Pump, Rotary $6,500 PD Pumps, Diaphragm $5,000 Total Equipment Cost $129,500 The largest equipment cost comes from purchasing the bath sonicator. Part of the manufacturing cost includes the standard shipping rates. These are shown in Table 7. Table 7. Shipping Specifications Object Quanity Price Price per Unit 16oz bottle 100 $40 $0.40 Cosmetic Labels 525 $38 $0.07 Shipping Rate $.30 per lb $5.95 per shipment The manufacturing plant will be located in the Southwest U.S. Table 8 shows different locations in Arizona that were considered for the manufacturing location. Table 8. Manufacturing Locations City Land Cost Distance from Phoenix Population Scottsdale, AZ $690, miles 23 minutes 200,000 Phoenix, AZ $515,000 0 miles 0 minutes 1,461,575 Mesa, AZ $430, miles 25 minutes 396,375 Cave Creek, AZ $425, miles 43 minutes 4,884 Peoria, AZ $423, miles 23 minutes 108,364 Glendale, AZ $415,000 9 miles 17 minutes 225,000 Chandler, AZ $375, miles 29 minutes 176,581 Apache Junction, AZ $311, miles 4hrs 40 minutes 31,814 Queen Creek, AZ $287, miles 45 minutes 4,316 Casa Grande, AZ $180, miles 51 minutes 25,224 Buckeye, AZ $160, miles 42 minutes 25,406 From the list of property costs Buckeye, AZ was selected as the plant location. The average utility costs and labor costs for Buckeye and the Southwest are included in the Total Product Cost as shown in the Economic Analysis

11 4.0 CONSUMER PREFERENCE MODEL In order to quantify consumer preferences, a model was developed based on the properties of the lotion. This model has the same form as the one proposed by Bagajewicz (2007). We first start with defining the consumer satisfaction score of product i (S i ) as the weighted average of normalized scores of different consumer related properties (y i,j ). S i = yi, j wi (1) where w i are the weights of importance for a respective property. The scores are typically defined as fractions in the range from zero to one. It is important to notice that these are properties defined in plain terms and assessed by consumers using their own knowledge and awareness of a given property. These properties are listed in Table 9, with a reference to which physical/transport property they are directly linked to. We now discuss each of these in detail, including the way the consumer assessed these properties. Table 9. Consumer and Physical Properties Consumer Properties Thickness Adhesion Spreadability Effectiveness Absorption Rate Smoothness Greasiness Physical Properties Relative Viscosity and Shear Rate Work of Adhesion Spreading Coefficient Intercellular Diffusion Intercellular Steady State Diffusion Time Greasiness Amount of Fatty Oils Approximately 100 potential consumers were asked to rate the lotions properties outlined in Table 9 using an ordained survey. This evaluation was estimated based on a small scale informal market analysis. The consumer rated their first preference, second preference, third preference, etc. on each of the seven properties assessed in this lotion. Each property was rated on the basis of a property rating measurement from one extreme to the next (e.g. very thin to very thick) The consumer confirmed their preference for each of the consumer ratings (i.e. their first preference to have a very thick lotion, moderately thick lotion, moderately thin lotion, or a very thin lotion, their second preference from the remaining consumer ratings, then their third preference, etc.). Given the rating measurement scales the consumer indicated the preference of each rating. At the

12 end of the survey the participants were asked to specify the relative importance of each property to them. The results of the relative importance of each property are shown in Table 10. Table 10. Relative Importance Consumer Property Weight of Importance Thickness 10.52% Adhesion 15.08% Spreadability 10.18% Effectiveness 24.49% Absorption Rate 13.76% Smoothness 14.55% Greasiness 11.41% A consumer preference vs. satisfaction curve was created to know what lotion formulation satisfies the most consumers. The consumer rating was subsequently connected to an underlying physical property as outlined in Table 9. We now discuss each property in detail. 4.1 THICKNESS The thickness of a lotion is an important property that can be related to the lotion s efficiency, stability and consumer acceptability. 5 The largest determinant for thickness is viscosity. The viscosity of the lotion was determined by using various relationships between the dispersed phase viscosity and the continuous phase viscosity. The dispersed phase in the case of a lotion will be the phase that is present in fine droplets (i.e. the insolubles). The continuous phase contains the ingredients that are soluble in aqueous solutions. Thus, the method used to determine the viscosity of the lotion, relied heavily on the dispersed phase concentration. 7 The relative viscosity of the lotion, η r, was determined in order to relate the effective dispersed phase viscosity to the continuous phase viscosity as outlined in Equation 2. 7 η η r = (2) η c where η r is the relative viscosity, η is the effective viscosity for the dispersed phase, and η c is the continuous phase viscosity. Equation 2 or the Taylor Relation can be used to

13 describe the behavior of the relative viscosity for dilute emulsions, assuming that the dispersed phase is composed on spherical droplets. 7 Not incorporated within Equation 2 is the affect of the interaction between droplets in the dispersed phase. This dimension can be examined and accounted for by using the following equation: η = 1 φ[ I( λ)] (3) r + where φ is the volume fraction of the dispersed phase. Lambda can be calculated using the following correlation: 1 3 λ = φ (4) The function I(λ) can be calculated as follows 7 ( 1 λ ) λ + 10 λ + 11 κ I ( λ) = (5) ( 1 λ ) 25λ ( 1 λ ) + ( 1 λ )( 1 λ ) κ where κ is the viscosity ratio between the dispersed phase and continuous phase, respectively. Summarily, Equation 3 shows that the relative viscosity depends heavily on the viscosity ratio and the dispersed phase volume fraction. Even though thickness is most often related to the viscosity, there are other parameters that must be assessed to fully grasp the apparent thickness of the lotion. According to The Handbook of Cosmetic Science and Technology, as the viscosity profile changes, so will the applicability of the shear stress and shear rate. The apparent viscosity of a lotion is defined by the equation below τ η = (6) D

14 where η is the apparent viscosity in Nm -2 s, τ is the shear stress in Nm -2, and D is the shear rate in s -1. The lotion s thickness can be related to the shear rate in the following manner: dv D = (7) dy where dv is the change in velocity and dy is the lotion thickness or film thickness. 6 The viscosity-shear rate profile differs among fluids. Emulsions, such as lotions, commonly show rheological behavior common to psuedoplastic fluids. 5 A psuedoplastic fluid is a fluid in which an increase in the shear stress will cause a decrease in the shear rate. 5 The rheological behavior of a psuedoplastic fluid is shown in Figure 3. Viscosity vs. Shear Rate Visocosity (Poise) Shear Rate (1/s) Figure 3: Viscosity vs. Shear Rate (Values taken from The section indicated as the Shear-Thinning Region is the region within a psuedoplastic fluid that shows a decrease in apparent viscosity when there is an increase

15 in shear. 5 This region is the most applicable region for our lotion, since this is a desirable quality for lotions. Basically consumers want a lotion that appears thick; yet, the lotion can be easily rubbed into the skin. 5 Since the shear rate is calculated from the film thickness and the sliding speed of the lotion s applicability, the thickness of the lotion can be determined. 6 The film thickness of the lotion was determined by assuming a sliding speed of 0.01cm/sec. Table 11 outlines the correlation made to determine the lotion s thickness. Table 11: Thickness Correlations Viscosity (Poise) Shear Rate (1/s) Film Thickness (cm) Consumer Rating Rating Number Extremely Thick Moderately Thick Moderately Thin Extremely Thin 4 As indicated by Table 11 and Figure 3, as the viscosity decreases the shear rate will increase. Furthermore, an increase in the shear rate produces a decrease in the film thickness. A correlation was made to determine the degree of lotion thickness. For example, a film thickness of 1cm is considered extremely thick and a film thickness of 0.001cm is considered extremely thin. A rating number was then corresponded to each consumer rating. The rating numbers are independent of rating scores on preferences. These are mere numbers used to categorize the parameters into a given consumer rating. For example, if the film thickness is cm. The following equation is used to determine how thick the lotion is. y = ln( x) + 1 (8) Using Equation 8 the consumer rating will be Correlating this value to the rating numbers outlined in Table 8, it is shown that a lotion with a film thickness of cm is extremely thin. Figure 4 shows an illustration of this relationship

16 Consumer Rating of Film Thickness 4 y = Ln(x) + 1 R 2 = 1 Consumer Rating Film Thickness (cm) Figure 4: Consumer Rating of Thickness Figure 4 indicates that a rating number of 1 has a film thickness of 1cm. This has been designated as extremely thick. Moreover, a rating number of 3 corresponds to a film thickness of 0.01cm. This has been categorized as moderately thin. The consumer ratings were subsequently correlated to a satisfaction score. The satisfaction score was determined from a study population of 92 people who completed an ordained survey rating their preference in the thickness of a lotion. Table 12 outlines the results of the survey. Table 12: Thickness Survey Results Extremely Thick Moderately Thick Moderately Thin Very Thin Raw Score Raw Percentage 32.61% 78.26% 64.13% 24.64% Adjusted Percentage 41.67% % 81.94% 31.48% The surveys were completed by having men and women determine their first, second, third and fourth preferences for their lotion thickness based on the consumer ratings (extremely thick to very thin). A low raw score indicates that a given consumer rating was more preferred than another. The raw scores were determined by adding up the preference scores for all of the survey participants. Likewise, the higher the raw score,

17 the least preferred a rating was to the consumers. The raw scores could range anywhere between 92 and 368. If a raw score of 92 was achieved this means that 100% of the survey participants said a given consumer rating is the most preferred product. Likewise, the lowest raw score will mean everyone preferred that type of product last in comparison to all the other choices. The raw percentages reflect the actual amount of people who would prefer a product with the given consumer rating. As Table 9 shows a moderately thick lotion is the most desirable to consumers. The raw percentage score, furthermore, reflects that no one product will be the best to everyone. The adjusted percentage is a relative percentage to the highest raw percentage. This shows how much of the population the product will satisfy if is has the indicated consumer rating. The adjusted percentage was correlated to the consumer ratings as illustrated in Figure 5. Consumer Preferences: Adjusted Thickness % 80.00% Consumer Satisfaction 60.00% 40.00% 20.00% y = x x x R 2 = % Consumer Rating Figure 5: Consumer Preferences for Adjusted Thickness Just as Table 11 showed, a consumer rating of approximately 2.25 is the type of product that will satisfy the most consumers. This consumer rating refers to a lotion that is moderately thick

18 4.2 ADHESION Adhesion is a lotion property that identifies how long the lotion will last on the skin. A lotion s adhesion depends on the adhesion wetting capabilities. Wetting is an application of adsorption at a liquid-solid interface. 5 Wetting is defined as the displacement of one fluid by another on a given surface. 5 Considering the lotion product, the emulsion displaces the air that is on the surface of the skin. The degree of wetting can be adjusted by adding surface-active particles (commonly known as surfactants or emulsifying agents) to decrease the interfacial tension of the fluid. Nevertheless, the degree of wetting is a function of the interfacial surface tensions of the dispersed phase to the continuous phase, the interfacial surface tension of the emulsion with the skin, and the contact angle of the emulsion to the skin. Surface tension is a chemical property that measures the force acting in a liquid surface along a specified length. 5 Moreover, surface tension is a parameter in fluids that is seen because of an imbalance in Van der Waals forces at a liquid interface(e.g liquid-liquid interface, liquid-gas interface and liquid-solid interface). 5 Moreover, a liquid s surface tension at its interface can describe a liquids behavior at other interfaces. The surface tension of the lotion s ingredients was determined by using the following correlation: σ 4 = P( ρl ρv) (9) where σ is the ingredient surface tension, P is the parachor based on the molecular structure of the ingredients, and ρ is the density for the liquid phase (l) and the vapor phase (v). 10 At low pressures the vapor density is negligible. Thus, the vapor densities were discarded in the calculation of the ingredient s surface tension. The surface tension of the emulsion was determined from Young s Equation 11 γ γ = γ cos( θ owp ) (10) op wp e

19 where γ is the surface tension of the phases, and θ is the contact angle of the surfactants to the dispersed phase. Young s Equation shows the difference in the surface tension of the oil-particle interface (op) and the surface tension in the water-particle (wp) equals the surface tension of the emulsion (e) multiplied by the contact angle. The mentioned particle in the interfaces is the emulsifying agents or surfactants used in the lotion. After the emulsion s surface tension is determined, the surface tension of the emulsion on the skin is identified using Young s Equation again. 12 This correlation is shown in Equation 11. γ se = γ γ cos(θ ) (11) s e where (se) is the surface tension at the skin-emulsion interface, (s) is the surface tension of the skin-air interface, and (e) is the surface tension of the emulsion-air interface. The contact angle shown in Equation 11 is the contact angle the emulsion makes with the skin. An analysis of contact angles are shown in Figure 6. Figure 6: Contact Angles and Wetting

20 A contact angle of θ = 0 o corresponds to complete wetting. As Figure 6 shows, a contact angle of θ = 180 o means that no wetting has occurred. It is best to have a contact angle less than 90 o. Adhesion, more specifically, can be described as adhesional wetting. Adhesional wetting examines the situation of a how well a fluid adheres to a substrate. 9 Furthermore the work of adhesion (W adh ) describes the reversible work necessary to separate a fluid from a substrate. 9 A mathematical correlation for the adhesional work is shown in Equation 12. Wadh = γ + γ γ (12) SA LA LS where W adh is the adhesional work, and γ is the surface tension of the skin-air interface (SA), the liquid-air interface (LA), and the liquid-skin interface (LS). Equation 12 is known as the Dupre Equation. 5 From the Dupre correlation it is identifiable that a reduction in the interfacial tension between lotion and the skin, will cause a greater tendency for adhesion. Whenever an interface includes a solid, the contact angle must be incorporated in the equation. 5 Since Young s Equation gives the following correlation γ LA cos( θ ) = γ γ (13) SA SL Dupre s Equation can be transformed into ( cos( ) + 1) W = θ (14) adh γ LA The work due to adhesional wetting can never be negative. A work equal to zero is obtained when the contact angle of the emulsion is θ = 180 o. In order to identify the adhesion of the lotion, the contact angle was related to the adhesion work. The following equation was derived from varying the contact angle in Equation 13 from 0 o to 180 o

21 3 2 y = x x x (15) where y is the work of adhesion and x is the contact angle. The work of adhesion was subsequently varied with the consumer rating. Table 10 shows the correlations made for the adhesion property. Table 10: Adhesion Correlations Contact Angle (Rad) Relative Work of Adhesion Consumer Rating Rating Number (π) 0% 0% Adhesion (5π/6) 6.7% 7% Adhesion (2π/3) 25% 25% Adhesion (π/2) 50% 50% Adhesion (π/3) 75% 75% Adhesion (π/6) 93% 93% Adhesion % 100% Adhesion 7 The contact angles were taken every π/6 radians (i.e 30 o ). From this table the contact angle was related to the consumer ratings as shown in Figure 8. Consumer Rating: Durability Consumer Rating y = x + 7 R 2 = Contact Angle (Rad) Figure 8: Consumer Rating of Adhesion

22 From Figure 8 it can be seen that a lower contact angle corresponds to a better adhesional capabilities. The consumer ratings were next related to a satisfaction score determined by an ordained survey completed by 94 participants. Figure 9 identifies the type of product that will satisfy the most consumers. Consumer Preferences: Adjusted Durability % % y = Ln(x) R 2 = Consumer Satisfaction 80.00% 60.00% 40.00% 20.00% 0.00% Consumer Rating: Durability Figure 9: Consumer Preferences for Adjusted Adhesion From Figure 9, the best lotion product is one where the adhesional work is large. Moreover, this occurs at the smallest contact angle possible. 4.3 SPREADABILITY Spreadability can be categorized as another dimension of wetting called spreading wetting. Spreading wetting is concerned with fluids that displace another fluid from a surface. Furthermore, spreadability is a fluid property that identifies the ease of a fluid to displace another fluid on a given surface. Spreading wetting can be differentiated if the spreading occurs spontaneously or not. 9 Spontaneity is a function of the surface free energy, surface tension and interface area. 9 For spreading to occur spontaneously, the

23 surface free energy has to decrease throughout the spreading of a fluid. 9 The surface free energy can be determined by the following equation: w [ γ ( γ + γ )] G = a (16) SA SL LA where - G is the total decrease in surface fee energy due to spreading wetting, a is the interface area, and γ is the surface tension of the skin-air interface (SA), skin-lotion interface (SL), and the liquid-air interface (LA). If the quantity SA ( γ γ ) γ + (17) SL LA is positive, then the change in surface free energy will be negative. This means the fluid will spread spontaneously. Moreover, the quantity expressed in Equation 17 is the measure of the spreading process driving force and is regarded as the spreading coefficient, S L/S. 9 Thus, if S L/S is positive, spreading will occur spontaneously. Contrarily, if S L/S is negative, the fluid will not naturally spread over a given surface. Factors affecting spreading are the relative surface tensions of the two fluids concerned. Furthermore, since the substrate on which the spreading is applied to is a solid, the contact angle of the lotion relative to the skin must be incorporated into the spreading coefficient correlation. 9 Thus, using Young s Equation, Equation 16 can be rewritten as ( cos 1) S (18) L / S = γ LA θ where θ is the contact angle of the liquid makes with the surface. When θ is finite, the quantity ( cosθ 1) (19) is always negative. Moreover, S L/S is always negative. The spreading coefficient will only be positive or zero when the contact angle is 0 o. 9 Considering the contact angle, a

24 positive S L/S means complete spreading wetting occurs. Contact angles other than 0 o reflect how easily the fluid can spread. The higher the contact angle, the harder it will be for the fluid to spread over a surface. Table 11 describes the correlation made between the spreading coefficient and the contact angle. Table 11: Spreadability Correlations Contact Angle (Rad) Spreading Coefficient Spreading Capability Consumer Rating Rating Number % 0% Spreading % 7% Spreading % 25% Spreading % 50% Spreading % 75% Spreading % 93% Spreading % 100% Spreading 7 The spreading coefficient was determined using Equation 18 and different contact angles ranging from 0 to π every π/6 radians. The spreading capability is a relative measure of the spreading coefficients. Figure 10 depicts how the contact angle is related to the consumer preferences. Consumer Preference vs. Contact Angle 8 Consumer Rating: Spreadability y = x + 7 R 2 = Contact Angle (Rad)

25 Figure 10: Consumer Rating of Spreadability There is a linear relationship between the contact angle and the consumer ratings. A contact angle of π is related to the consumer rating 0 percent spreading. Moreover, a contact angle of π/2 is related to a consumer rating of 50 percent. After this correlation was made, the consumer rating was related to the consumer satisfaction established by an ordain survey completed by 92 participants. The survey results are shown in Figure 11. Consumer Preferences: Adjusted Spreadability % Consumer Satisfaction (%) 80.00% 60.00% 40.00% 20.00% y = x x x x R 2 = % Consumer Rating Figure 11: Consumer Preferences for Adjusted Spreadability The consumer rating is related to a consumer satisfaction in a quadratic manner. The best product is a lotion that has between 50 percent and 75 percent spreadability. This relays to a spreading coefficient of approximately or a contact angle between 90 o and 60 o. 4.4 EFFECTIVENESS The effectiveness of a lotion is a determinant of how well the lotion can treat the skin problems associated with Xerosis and Ichthyosis Vulgaris. As previously mentioned, the problems people face with these two conditions include:

26 Severely dry skin Thickened skin Dismantled lipid bilayer The skin hydration layer in the SC, the outer most layer of the skin is normally around 30 percent. 15 When the skin hydration level falls below 10 percent, the skin becomes severely dry and chapped. 13 Not only is keeping the skin hydration level around 30 percent important for an aesthetically pleasing skin, when the skin is adequately hydrated the desquamation process remains active and the skin acts as an effective barrier against infection. 15 When the desquamation process is hindered, dead skin cells are not renewed on the SC leading to a build up of dead skin cells. 13 This is what causes the skin to become thickened. Furthermore, the lipid bilayer surrounds hydrophilic cells in order to retain water within the skin. When the lipid bilayer is dismantled or ruptured, moisture from the skin is able to escape into the environment by transepidermal water loss (TEWL). 5 Examining all the parameters that need to fixed by the lotion, it is obvious that the effectiveness of the lotion is a function of the concentration of active ingredients into the SC. Modeling percutaneous absorption, the process by which chemicals are absorbed into the skin, is necessary to access transdermal drug delivery. 14 Percutaneous absorption incorporates transdermal transport because the chemicals that are absorbed into the epidermis partially into the dermis as well. 14 This is due to the fact that the epidermis does not contain any capillary vasculature. 14 Due to the absence of this aforementioned biologic structure, permeability into the epidermis is restricted. 14 As chemicals finally travel through the epidermis, they are able to reach capillary vasculature vesicles to enter the blood stream and partially enter the upper layers of the dermis. 14 Moreover, the SC has been identified as the primary barrier to percutaneous absorption. 14 The SC is associated with having poor permeability. This is due to the structure of the SC. The SC is composed of percent water, 20 percent lipids, and 40 percent

27 keratinized protein. 14 Structurally, the lipid bilayer surrounds the keratinized proteins, forming an intercellular matrix. 14 Furthermore, the structure of the SC, dictates its function. The compactness of the intercellular matrix prevents TEWL and harmful chemicals and antigens from entering the integumentary system. There are three routes that can be taken for percutaneous transport through the SC. These three pathways are illustrated in Figure 12. keratinocytes lipid lamellae Figure 12: Transdermal Transport Pathways 14 appendage (follicle or sweat duct) Pathway (1) consists of intercellular diffusion through the lipid lamellae, the intercellular spaces outlined in Figure Pathway (2) is transcellular diffusion through the keratinized proteins and the lipid lamellae. 14 Lastly, pathway (3) is characterized by diffusion through the skin appendages (i.e. hair follicles and sweat ducts). 14 The different models developed to characterize percutaneous absorption were stimulated based on these three pathways. Due to the compactness of the intracellular matrix, transcellular absorption (pathway 2) is a thermodynamically and kinetically impossible passageway for chemical transport. 16 Recent experiments show a higher susceptibility for percutaneous absorption to occur via intercellular diffusion through the lipid lamellae. 17 Thus, only the intercellular pathway was examined to determine the transdermal diffusion of the lotion s ingredients into the skin. Models of percutaneous absorption are based on the assumption that the skin is a homogeneous medium with a uniform permeability coefficient. 14 Flynn (1990) showed experimentally that permeability and diffusion depend heavily on the partition coefficient, K ow, and the molecular weight, MW

28 Intercellular diffusion is modeled as a three phase continuum in the SC as depicted in Figure 13. Figure 13: Intercellular Diffusion Three Phase Continuum Intercellular diffusion has an immobile phase consisting of the keratinized proteins. The two other phases in the continuum are mobile phases composed of the oil (o) and water (w) phases within the lipid lamellae. Diffusive transport within the mobile phases was assumed to be governed by Fick s Law. The following partial differential equation was correlated to identifying a chemical s concentration within each phase of the continuum: t Co Cw ( C + C φ + C φ ) = D τ φ + D τ φ oφ 0 0 w w p p o o w w w (20) x x x where C is the chemical concentration of the respective phases (p,o,w), φ is the porosity of the respective phases, D is the molecular diffusion coefficients of the respective phases, τ is the tortuosity coefficient relating the linear transport distance to the actual transport distance, t is the time, and x is the penetration distance into the skin. After several correlations were made between the partition coefficients and the chemical concentration for each phase, Equation 20 was rewritten in terms of the water phase components. 2 C w Dsc Cw = (21) 2 t Rsc x

29 where D sc is the average diffusion coefficient for the three phase SC (sc) continuum and R sc is the retardation factor for the three phase SC continuum. Equation 21 was transformed again after several boundary and initial conditions were identified. The concentration of the water phase is correlated as a function of time, penetration depth into the skin, and several other diffusive properties. C C w o w = 1 x L sc 2 π n= 1 1 nπx sin e n Lsc 2 2 D sc n π t 2 R L sc sc (22) where C o w is the chemical concentration on the surface of the SC. This concentration is assumed to be constant. 14 For most ingredients, the summation part of Equation 22 was approximately zero. Moreover, L x = sc (23) 2 Thus, the highest relative concentration found within the SC was 0.5. Correlations were subsequently made to relate the relative concentration of the water phase for the SC to consumer ratings. The results are shown in Table 12. Table 12: Effectiveness Correlations C/Cw o Consumer Rating Rating Number 0.1 Very Scaly Moderately Scaly Some Scales Few Scales No Scales 1 Table 12 shows that the higher the water phase concentration in the SC continuum, the less amount of chapped, scaly skin is present. Figure 14 shows the results of Table

30 Consumer Rating vs. Relative Concentration 5 Consumer Rating y = -10x + 6 R 2 = Relative Concentration (C/Cw) Figure 14: Consumer Rating of Relative Concentration Figure 14 shows that there is a linear relationship between the consumer rating and the relative chemical concentration. As Figure 14 and Table 12 suggests, a relative concentration of 0.5 is associated with a consumer rating of 1. Likewise, a relative concentration of 0.2 is associated with a consumer rating of 4. The consumer ratings were subsequently related to a consumer satisfaction based on ordained surveys completed by 95 participants. The results are shown in Figure

31 Consumer Preferences: Adjusted Effectiveness % 80.00% Consumer Satisfaction 60.00% 40.00% 20.00% y = x R 2 = % Consumer Rating Figure 15: Consumer Preferences for Adjusted Effectiveness Figure 15 also identifies a linear relationship between the consumer rating and the consumer satisfaction. The best product appears when the relative concentration of the water phase is at a maximum. 4.5 ABSORPTION RATE The absorption rate for the lotion is reflective of the steady state diffusion time necessary for percutaneous absorption to occur. According to the diffusion correlation made to determine the lotion s effectiveness, the absorption rate (t sc ) of the lotion is a function of the mass flux of chemicals into the bloodstream (m sc ) and the amount of mass transferred per unit area (Q sc ). 14 The mass flux of the lotion s ingredients through the epidermis can be determined by applying Fick s Law. 0 D = + sccw 1 2 Lsc n= 2 2 Dscn π t. n 2 Rsc Lsc sc m 1 ( 1) e (24)

32 where D sc is the diffusion coefficient, C 0 w is the ingredient concentration on the surface of the skin, L sc is the distance from the surface of the SC, and R sc is the retardation factor for the SC water phase continuum. The overall amount of ingredients that has completed transdermal transport in mass per unit area is determined by the following equation: Q sc = t. msc 0 dt (25) After completing the integral, the following correlation determines the absorption rate time: t Q L R 2 0 sc sc sc sc = 0.45 (26). D sc sc m Equation 23 can be easily converted from seconds to minutes. Thus the relative preference for a range of absorption rates were determined by ordained surveys completed by 95 participants. The results are shown in Figure 16. Consumer Preferences: Adjusted Absorption Rate % Consumer Satisfaction % 80.00% 60.00% 40.00% y = x x x R 2 = % 0.00% Absorption Rate (min) Figure 16: Consumer Preferences for Adjusted Absorption Rate

33 The absorption rate is related to a consumer satisfaction in a cubic manner. A solution that takes no time to a little over two minutes to absorb is the most desirable product. 4.6 SMOOTHNESS Skin smoothness is commonly associated with healthy, hydrated skin. When the skin becomes dry, the skin often takes on a rough texture. This inherent roughness is due to transepidermal water loss (TEWL) in the SC. 5 TEWL usually occurs when there is a sudden decline in the moisture content of the air or if the skin was in recent contact with water or detergent solutions. 5 Furthermore, the onset of dry skin is condition associated with the SC. 5 Often times chapping occurs to the SC when the skin is dry. 5 Chapping basically is the superficial cracks seen on the skin, making the skin appear scaly. 5 Furthermore, the chapping of the skin occurs because the SC swells as it rapidly absorbs water into the skin to offset the low skin hydration level. 5 This swelling process places overbearing stress to the skin, causing splits and cracks to form on the surface. 5 The combination of a decreased hydration level as well as skin chapping constitutes skin roughening. 5 When the skin is removed from or depleted of its moisture source (moist environment, water or detergent solution), the SC begins to dry and return to its original size and form. 5 Nevertheless, since the swelling in the SC produces cracks and splits to the skin s surface, not all skin cells are able to return to its original form. 5 This discontinuity among the skin cells (the cells able to retain their size and shape against the cells that are not able to reform) gives a rough feel to the skin. 5 A characteristic of dry skin is a feeling of loss of natural oiliness. 5 The skins natural oils come from the natural moisturizing factors (NMF). 5 The NMF of the skin act as the SC s natural humectant, which attracts and binds water to the skin. Moreover, the NMF has been shown to act as a plasticizer, providing a softening effect. 5 Moreover, NMF aid in the plasticization of the skin by making the skin more hydrated and flexible. 5 Two conditions (hydrated skin and flexible skin) definitely needed to prevent roughening of the skin. The NMF are commonly removed from the skin either when the skin is

34 immersed in water and/or when the skin is exposed to a detergent solution. 5 Thus when the skin loses its natural humectancy, the condition known as dry skin occurs. The skin can replenish it s natural smooth feeling by applying certain low friction, oily materials to the skin. 5 Humectants can also be added to the skin to compensate for losing the NMF that are associated with giving skin a smooth feel. 5 Occlusives also can be added to the skin in order to form a continuous oil phase at the skin s surface. 5 This will aid with TEWL by providing a higher moisture content to prevent the onset of dry skin. Of the suggested remedies, it is easily seen that most of the ingredients necessary to achieve smooth skin is to prevent the onset of dry skin. Dry skin can be reduced and prevented by having a certain amount of oils and insolubles present in the lotion to absorb and remain on the skin s surface. Another active ingredient that has been associated with softening the skin through rehydration includes emollients. 5 Emollients are oily materials that prevent TEWL by filling the intercellular spaces of the ruptured lipid bilayer. Thus oily materials and humectants are necessary to give the skin a smooth feel. Summarily, smoothness is dependent on the greasiness or oiliness of the lotion. Through experiemental analysis, the following correlation was made to determine the skins smoothness with a certain greasiness level. S = 0.236( G ) (27) where S is the skin s smoothness and G is the moisturizer s greasiness level. Table 13 outlines the correlations necessary to fully assess the smoothness of the skin after the lotion is applied. Table 13: Smoothness Correlations Greasiness (%) Smoothness Consumer Rating Rating Number Very Smooth Moderately Smooth

35 Moderately Rough Very Rough 4 Table 13 and Equation 27 show that there is an inproportional relationship between the greasiness and smoothness. The smaller the smoothness is found to be the smoother the skin will become. The consumer ratings were correlated to certain rating numbers in order to categorize how the smooth the skin will become with a certain greasiness level. The points from Table 13 are illustrated in Figure 17. Consumer Rating vs. Smoothness Consumer Rating 4 y = x R 2 = Smoothness Figure 17: Consumer Rating of Smoothness Lastly the consumer ratings were correlated to a consumer satisfaction. The consumer satisfaction scores based on consumer ratings were determined from ordained surveys completed by 95 study participants. The results of the survey are shown in Figure